Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyLet fbe a value in the range140 · ️Given real function is f(x) = x/1x^2 ️1 x^2 ≠ 0 ️x^2 ≠ 1 ️Domain x ∈ R ️Let f(x) = y ️y = x/1x^2 ️⇒ x = y(1 x^2) ️⇒ yx^2 – x y = 0 ️This is quadratic equation with real roots ️(1)^2 – 4(y)(y) ≥ 0 ️1 – 4y^2 ≥ 0 ️⇒ 4y^2 ≤ 1 ️⇒ y^2 ≤1/4
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F(x)=1+x^2 find domain and range-What is the domain and range of the real function f(x)=1/(1x^2)?SOLUTION find the range and domain f (x)=1/x2 Question find the range and domain You can put this solution on YOUR website!
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Algebra Find the Domain and Range f (x)=1/ (x1) f (x) = 1 x − 1 f ( x) = 1 x 1 Set the denominator in 1 x−1 1 x 1 equal to 0 0 to find where the expression is undefined x−1 = 0 x 1 = 0 Add 1 1 to both sides of the equation x = 1 x = 1 The domain is all values of x xSolution For Find the domain and range of f(x) = 1x 2 So, Range will be all the values less than or equal to zeroShow Solution We can observe that the horizontal extent of the graph is –3 to 1, so the domain of f f is ( − 3, 1 ( − 3, 1 The vertical extent of the graph is 0 to – 4 – 4, so the range
281 · What is the domain and range of this function?116 · Answer Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams Find the range of 6k 1k 314 Find the range ofIn this section, you will learn how to find domain and range of inverse trigonometric functions To make you to understand the domain and range of an inverse trigonometric function, we have given a table which clearly says the domain and range of inverse trigonometric functions
109 · Given that f(x) = 1/√(x 5) Here, it is clear that (x) is real when x – 5 > 0 ⇒ x > 5 Hence, the domain = (5, ∞) Now to find the range put For x ∈ (5, ∞), y ∈ R Hence, the range of f29 · Given f (x) = 1/√x−5 To find the domain and range of function Explanation So, the domain of a function consists of all the first elements of all the ordered pairs, ie, x, so we have to find the values of x to get the required domain Given, f (x) = 1/√x−5 Now for real value of x5≠0 and x5>0 ⇒ x≠5 and x>5 Hence the domain of f = (5, ∞)Hence, for the trigonometric functions f (x)= sin x and f (x)= cos x, the domain will consist of the entire set of real numbers, as they are defined for all the real numbers The range of f (x) = sin x and f (x)= cos x will lie from 1 to 1, including both 1 and 1, ie 1 ≤ sin x ≤1
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–1 x 2 4 y 021 Mathematics Learning Centre, University of Sydney 5 State its domain and range Solution The function is defined for all real xThe vertex of the function is at (1,1) and therfore the range of the function is all real y ≥ 1 12 Specifying or restricting the domain of a function · For any real values of x, f(x) will give defined values Hence the domain is R Since we have absolute sign, we must get only positive values by applying any positive and negative values for x in the given function So, the range is 0, ∞) Question 2 Find the domain and range of the following functions f(x) = 1 x 2 Solution For · Find the domain and range of f (x)=x2/1x2 Domain of the function is where the function is defined The given function X R Let fx y y x1x2 x y1 x2 yx2 x y 0 This is quadratic equation with real roots Find the domain and range ƒx 1 x2 Maintain the following steps 1 QUESTION 2 Find the domain of the function fxy
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Let Then means that because the denominator cannot be 0 So the domain of f is To find the range, get x in terms of y So clearly, Then because it is a square, This means that Then either because that makes or because that makes a unit fraction that is smaller than 1 So,Find domain and range of `f (x)=x/ (1x^2)` Find domain and range of `f (x)=x/ (1x^2)` Watch later Share Copy link Info Shopping Tap to unmute If playback doesn't beginAlgebra Find the Domain and Range f (x)=1/x f (x) = 1 x f ( x) = 1 x Set the denominator in 1 x 1 x equal to 0 0 to find where the expression is undefined x = 0 x = 0 The domain is all values of x x that make the expression defined Interval Notation
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Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack Exchange5217 · Moreover, the square of a number in the domain is at most $1$, so $1 x^2 \geq 1 1 = 0$ Since a polynomial function is continuous, $1 x^2$ assumes every value in the interval $0, 1$, so we have $0 \leq 1 x^2 \leq 1$ Taking square roots yields $0 \leq \sqrt{1 x^2} \leq 1$, so the range is $0, 1$Solution to Example 4 The domain of this function is the set of all real numbers The range is the set of values that f (x) takes as x varies If x is a real number, x 2 is either positive or zero Hence we can write the following x 2 ≥ 0 Subtract 2 to both sides to obtain x 2 2 ≥ 2
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So the range is Rf 0g (h) f(x) = 1=(x 1) The domain is R f 1gas we cannot let x= 1 (why?) So as xtakes values in the domain what values do we get for f(x) = 1=(x 1)?Arithmetic Mean Geometric Mean Quadratic Mean Median Mode Order Minimum Maximum Probability MidRange Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution Physics Mechanics domain f(x)=\frac{1}{x1} en Related Symbolab blog posts My Notebook, the Symbolab wayAnswer Under square root the polynomial must be positive The domain is obtained by solving You can obtain the zeroes of the polynomial So the polynomial is solved in the external intervals Since the function f (x) is positive, due to result of square root, The range includes all positive real numbers x≥ 0 Hence, this is the answer
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Given f (x) = 1/𝑥 , x ∈ R – {0} Finding f (x) at different values of x f (−2) = 1/ (−2) = – 05 f (−15) = 1/ (−15) = −10/15 = −2/3 = – 066 f (−1) = 1/ (−1) = −1 f (−05) = 1/ (−05) = −10/5 = – 2 f (025) = 1/025 = 100/25 = 4 f (05) = 1/05 = 10/5 = 2 f (1) = 1/1 = 1 fAnswer The domain is all real numbers, and the range is all real numbers f(x) such that f(x) ≤ 4 You can check that the vertex is indeed at (1, 4) Since a quadratic function has two mirror image halves, the line of reflection has to be in the middle of two points with the same y valueFor example, a function f (x) f ( x) that is defined for real values x x in R R has domain R R, and is sometimes said to be "a function over the reals" The set of values to which D D is sent by the function is called the range Informally, if a function is defined on some set, then we call that set the domain
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Putting it all together, this statement can be read as "the domain is the set of all x such that x is an element of all real numbers" The range of f(x) = x 2 in set notation is R {y y ≥ 0} R indicates range When using set notation, inequality symbols such as ≥ are used to describe the domain and range Therefore, this statement can be read as "the range is the set of all y such that y is1 See answer rozolynnt is waiting for your help Add your answer and earn points cathylaureano94 cathylaureano94 Answerdomaine =f range = x Stepbystep explanationi think New questions in MathematicsThis is the Solution of Question From RD SHARMA book of CLASS 11 CHAPTER RELATIONS AND FUNCTIONS This Question is also available in R S AGGARWAL book of CLAS
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281 · Hence, both its domain and range should be real numbers x can be a number from –3 to 3 f(x) is between 0 & 3 Hence, Domain = Possible values of x = Any number from −3 to 3 = −3, 3 = {x −3 ≤ x ≤ 3} Range = Possible value of f(x) = Any number from 0 to 3 = 0, 3 = {x 0 ≤ xDomain\f (x)=\frac {1} {x^2} domain\y=\frac {x} {x^26x8} domain\f (x)=\sqrt {x3} domain\f (x)=\cos (2x5) domain\f (x)=\sin (3x) functiondomaincalculator domain f (x)=\frac {1} {xDomain and range of a function and its inverse When a function has no inverse function, it is possible to create a new function where that new function on a limited domain does have an inverse function For example, the inverse of f ( x) = x \displaystyle f\left (x\right)=\sqrt {x} f (x) = √
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Question State the domain and range of f^1 (x), given f(x)=(x1)^2 2 ** Please note their should be brackets around x1 part** I'm not sure if the brackets will show up for you This is what I have tried so far · The domain is simply the denominator set equal to 0, {xl x≠3} However, range is found by solving for (isolating x to one side) and setting the denominator equal to zero x = 3 1 y So range is {xl x≠0} No, it would be {y y ≠ 0} I find it helpful to memorize the domains and ranges of some of the parent functionsSet the denominator equal to zero Remember, dividing by 0 is undefined So if we find values of x that make the denominator zero, then we must exclude them from the domain Now to find the range, notice that
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Let us find the values of the range and domain for the function〖 tan〗^(1)nx Let us observe how the values of the range and domain get changed when we change the values of tan nx & tan^(1)nx Let us change the value of n and observe at which value along the xaxis we get the maximum and minimum values of the graphIf f is a function of two variables with domain D, then the graph of f is the set of all points (x;y;z) in R 2 such that z = f(x;y) and (x;y) is in D P Sam Johnson Domains and Ranges of Functions of Several Variables 6/78Rational functions f(x) = 1/x have a domain of x ≠ 0 and a range of x ≠ 0 If you have a more complicated form, like f(x) = 1 / (x – 5), you can find the domain and range with the inverse function or a graph See Rational functions Sine functions and cosine functions have a domain of all real numbers and a range of 1 ≤ y ≤ 1
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Table of Domain and Range of Common Functions A table of domain and range of common and useful functions is presented Also a Step by Step Calculator to Find Domain of a Function and a Step by Step Calculator to Find Range of a Function are included in this website · The domain and range of the function f(x) = x 2 has to be determined The domain of a function is all values of x for which the value of f(x) is definedDomain and Range The domain of a function f ( x ) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes (In grammar school, you probably called the domain the replacement set and the range the solution set They may also have been called the input and output of the function)
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This is a revised answer!The domain and range of the function f= ((1/1x2)) x ∈ R, x ≠ ± 1 are respectively Q The domain and range of the function $f=\left\{\left(\frac{1}{1x^{2}}\right) x \in R, x · Find the Domain and Range f(x) = log of x12 f (x) = log (x − 1) 2 f(x)=log(x1)2 Set the argument in log (x − 1) log(x1) greater than 0 0 to find where the expression is defined x − 1 > 0 x1>0 Add 1 1 to both sides of the inequality x > 1 x>1 The domain is all values of x x that make the expression defined
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Click here👆to get an answer to your question ️ Find the domain and range of f (x) = √(16 x^2)What are the domain and range of f(x)=(1/5)x?For the reciprocal squared function \(f(x)=\dfrac{1}{x^2}\),we cannot divide by 0, so we must exclude 0 from the domain There is also no x that can give an output of 0, so 0 is excluded from the range as well
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