How do you determine if a function f (x) has an inverse on an interval (a, b)?

Q: (a) If f(x) = V3 – x, find the inverse function f. %3D

A: Topic = Functions

Q: Construct a table of values for the function f(x)=x²-1 in the restricted domain {x|0≤x≤4}.Is f a one…

A:

Q: Are f(x)=3x+5 and g(x)=(x/3)-5 inverse functions? Use function composition.

A:

Q: what is the inverse of the function below?

A:

Q: Find the inverse function of f. f(x) = 3 Fx) =

A:

Q: Let (-x² when x 0 (a) Is f increasing? (b) Does f have an inverse? If so, what is it?

A:

Q: Let f(x) = (x−³+4)5 – 1.

A: Assume that y=f(x) and use the description of f(x) and then express x in terms of y, that formula in…

Q: Let f(x)=x+4/x+8 f^-1(−7)=   the f^-1 just means inverse function

A:

Q: Find the inverse of the function f(x) = x². f- (7) The domain of f- is |

A:

Q: can an even function be selv-inverse?an odd function?

A: Can an even function be self-inverse?an odd function?

Q: 2. Explain how we know the function f(x)= 2.x is one-to one. Then find the inverse function f. x- 3

A: We are asked to  find the inverse of the function.

Q: Verify graphically that the functions f(x) = 2x – 3 and g(x) = }(x + 3) : are inverse functions of…

A: Explanation: Given that,  f(x)=2x-3g(x)=12(x+3)       Concept Used: We know that , In case of…

Q: What is the inverse function of f(x) = x- 2 2x f-'(z) = - (z) = I- 2 f (2) = 2x f (x) = r - 1

A: Replace f(x)by x and x by y than solve for y.

Q: Determine whether the function has an inverse function. 2 f(x) = %3D

A:

Q: b. What would be another acceptable way to restrict the domain of the inverse function?

A: We have, y = sinx  So, x = sin-1(y)

Q: What is the inverse function of f(x) = 2 + Vx-1? O (x+2) - 1 O (x-2) +1 O (x- 1)2 +2 O (x+ 1)? - 2

A: f(x) = 2+x-1let y = f(x)so , x= f-1(y)Now, y=2+x-1y-2=x-1squaring  O.B.S(y-2)2=(x-1)2 (y-2)2 =x-1

Q: What is the inverse of the function h(x): x + 4? h-1(x) = |

A:

Q: What is the inverse of the function f(x) = e\? %3D

A:

Q: Find the inverse function of f. f(x) = 3 – 2x %3D - f-1(x) = %3D

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: 3. Find the rule for the inverse of f(x) = X +1

A: Inverse of functions is given.

Q: Find the inverse of the function. (Enter the domain using interval notation.) f(x) = (x + 3)², x >…

A:

Q: What is the inverse of the function of g(x) = x^3

A:

Q: Find the inverse function of f informally. Verify that f( f −1(x)) = x and f −1( f(x)) = x. f(x) =…

A: Solution:Given   f(x)=x2-4   x≥0To find inverse the function and Verify that f( f −1(x)) = x and f…

Q: Solve for the inverse fonction of f(x)= domain and range of both. f and f . -1.

A:

Q: 3. Consider the two inverses you found above (or any function and its inverse). What is f(f-'(2))?.

A: let f(x) be any function and  the inverse of the function  f(x) is f-1(x). we know that f(x) and…

Q: f&)= /x-1 and gx) -x²+I

A:

Q: find the inverse function of f  f(x)= 2x-1/x-7 f^-1(x)=

A:

Q: Find the inverse function of r informally. (x) = x f-(x) = 3x Verify that f(f-{(x)) = x and f-(f{x))…

A: (i) fx=x3⇒x=3y ; f-1x=3x . (ii) ff-1x=f3x=13.3x=x  (proved) (iii) we have to find : f-1fx=f-1x3 Now,…

Q: What is the inverse function of In x, and what are its domain and range?

A: Inverse of lnx:A function g is the inverse of function f if for y=fx,  x=gy y=lnxx=lnyex

Q: Find the inverse function of f informally. Verify that f( f −1(x)) = x and f −1( f(x)) = x. f(x) =…

A: Find the inverse function of f informally. Verify that f( f −1(x)) = x and f −1( f(x)) = x.…

Q: 1 What is the inverse of the function y ? 2х + 3

A:

Q: A graphical test for the existence of an inverse function of f is the _______ Line Test.

A: We have given statement as   A graphical test for the existence of an inverse function of f is the…

Q: why or (a) Are f(x) = 3x –1 and g(x) = ¿(x – 3) inverse functions? Why %3D not?

A:

Q: The inverse of the function f: R - R defined by f (x) = x2- is

A:

Q: What is the inverse of a function from A to B under function composition?

A: Let f : A→B be a bijective function.

Q: Let f(x) = 2 – Væ + 5. What is the inverse of f?

A:

Q: Given the function f(x)= |x-1|: (a) explain why f(x)= |x-1| does not have an inverse function over…

A: Given fx=x-1

Q: Verify the inverse function theorem of function f(x) = 3x – 2. -

A: We have to fi nd the inverse function

Q: Let f(x) = (x − 2) / (x − 1) . Show that f is its own inverse function. What can you conclude about…

A: Given function, y=fx=x-2x-1

Q: What procedure can you sometimes use to express the inverse of a function of x as a function of x?

A: Consider f(x) to be a function of x.

Q: True or false? Explain. The function g (x)=-x is the inverse of the function f(x)=-x.

A: In this question we need to verify the given statement is true or false.

Q: Find the inverse function of f(x) = 3 + . f(z) =

A:

Q: Consider the function f (x) = /2x – 8. If ƒ -'(x) is the inverse function of f (x), find f -'(2).

A: let y=f(x)y=2x-8for inverse function, replace all x with y and y with xx=2y-8⇒2y=x+8squaring both…

Q: Let f(x) = 4 + 2x -cosx. If g(x) is the inverse function of f(x), then g’(3) = ?

A:

Q: Find the inverse function for f(x)= 2/x-1. Show all work.

A: Let the given function be written as,

Q: Find the inverse of the function on the given domain. f-1 (x) = f(x) = (x - 18)2, [18, ∞)

A: Inverse of function f(x)=(x-18)2 . In the interval [18, infinity) is  f-1(x)= 18+sqrt(x)

Q: 1- Vã y = x2-4x2 + 16V, x24 エ-2

A:

Q: Find the inverse function of f. f(x) = 7 – x², x 2 0 f-1(x) = %3D

A:

Q: Why do we restrict the domain of a function when we are finding the inverse? *

A:

Q: f(x) = x² is inverse function on integer number?

A: The inverse is f-1(x) = √x