let f(x)=1/2ln(1+x/1-x). compute the inverse function f-1 (x) and find its domain and range.

Q: 05:- Find the inverse function f-1(x) if exists in the following cases:- c) f(x) = 1-

A:

Q: Find the inverse function of f.

A: An inverse function is reverse of the given function. In simple words if a function f takes input…

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

A:

Q: etch the graphs of f(x) = √ −1 − x and its inverse function using the same coo

A: The equation of the graph is f(x)=-1-x

Q: Show that f (x) = x³ +1 is one-to-one and find its inverse function f-'(x).

A:

Q: Show that f(x) = |5x| has no inverse function.

A:

Q: find the inverse function. Show all work. f(x)= 2/x-3

A: The given function is,

Q: Find the inverse function of f.

A: Solution:Givenf(x)=x2+x,    x≥-12To find the inverse of the function:

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

A:

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

A: If we have two functions h(x) and g(x), such that h(g(x)) = g(h(x)) = x  Then, h(x) and g(x) are…

Q: if f(X)= SINX+2X+1 and g is the inverse function of f, what is the value of g'(1) ?

A:

Q: Find a formula for the inverse of the function. f(x) = 8 – x², x > 0 f-1(x) = %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: Find the equation for f-1, the inverse functions, of f(x) = 5x + 2. Verify that your equation is…

A: Solve as below

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: Find the domain of the function. f(x) = √(ln x)

A: To find domain of the function fx=lnx. Solution: Domain is the input value for which a function is…

Q: Find the inverse function of f.

A: f(x)=2+3+x

Q: Find a formula for the inverse function f -1 and verify that(ƒ ∘ f -1)(x) = (f -1 ∘ ƒ)(x) = x.

A: The given function is fx=1001+2-x. In order to find the inverse function, replace x by f-1x and fx…

Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: Given f(x)=In(x2 -1)-3 where x<-1, find its inverse function f -1(x).

A: Given that: f(x)=ln(x2-1)-3, where x&lt;-1

Q: Find the inverse function of f.

A:

Q: Let f be a function defined by f(x) = ln(3 − 2x). What is the maclaurin function expression of the…

A:

Q: Identify the inverse function. f(x)3D 2 Oo f(2) = *) In (2x F 2) = In[(2a)*| f(x)3 4ln(2x) f (z) =…

A: Given: f(x)=ex214 ; To find the inverse function:

Q: Find a formula for the inverse function of h(x)=2e3x . Verify that h-1(h(0))=0

A:

Q: Let f(x) = - x - 4x + 13 , x< - 2. Find a formula for the inverse function . %3D f"(x) = D -1

A: Given data

Q: 16. Find the inverse function of f. f(x) = x2 - 3, x 2 0 Then, use compositions of functions to…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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: Find the inverse function of f. f(x) = x³- 9 O s-'x) = Vx+9 %3D O f-'x) = Vx+ 9 O 5-x) = Vx- 9 O…

A: Given function fx=x5-9. The objective is to find the inverse function of f.

Q: Find the domain of the function: f(x) = ln(4 - x)

A: we have to find the domain of the given function. f(x)=ln(4-x)

Q: Find the inverse function of f(x) = /2x + 2. f-'(x) :

A: f(x)=2x+2 to find the inverse function.

Q: Find the domain of the function: f(x) = ln(3 - x)

A: The Domain of a function Includes all values of x for which the function is defined. We know that 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: Find the inverse function of f informally. Verify that f( f −1(x)) = x and f −1( f(x)) = x.…

Q: Find the inverse function of f(x) = 4x. Then verify that both f( f −1(x)) and f −1( f(x)) are equal…

A: Given a function f(x)=4x To find the inverse of f(x) First write the function as a linear function…

Q: Find the inverse function of f (x)= 4x, Verify that both 1) f (f-1(x) 2) f-1(f(x) are equal to the…

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Q: Find the inverse function of f(x) = /2x + 2. %3D f-'(æ) = ||

A:

Q: f(x)=3x+4x−1 .  Find the inverse function, f-

A:

Q: 05:- Find the inverse function f-1(x) if exists in the following cases:- b) f(x) =, x 0 x+1

A: Find function of y Then replace y as x

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

A:

Q: Find the inverse of the function f(x) = – 5x² . f-'(x) = The domain of ƒ-' is

A: Solution:- let f(x)=y

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: Consider the function f(x) = i + x². How does this function essentially behave for large positive…

A: The Given Function f(x) contains rational function x/(x2+1) and polynomial function function…

Q: Find the inverse function of f(x) = 19 + x. f-(x) =

A: We have to find the inverse function from the given function

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

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Q: let f(x)= 4x/2-x find inverse function of f

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Q: Let fAx) =x' 4x + 20. a) Explain using Calculus why f has an inverse function (invertible). b) If…

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Q: Find the inverse function f-1 of the function f f(x) = 8 tan(10x - 3)

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Q: how do I find the inverse function of f(x)=1/x?

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Q: Find the inverse function, f (x) for f (x) = %3D x+2

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.