Verify that f and g are inverse functions algebraically. f(x) = x3 + 5, g(x) = ∛(x − 5)

Q: Show that the function y = f (x) =-2x +4 is one-to-one and find its inverse function.

A: Here function  fx=-2x+4

Q: Find a formula for the inverse of the function. y = In(x + 3)

A: y=lnx+3

Q: Find a formula for the inverse of the function.  f(x) =  x 2  - x ,            x > =1/2

A: Given function:

Q: If g is the inverse function of f(x)   = 2x  + In  x,  find g'(2)

A:

Q: Find the inverse function of the function f(x)= 3x3 on the domain x > 0.

A:

Q: 3x +1 Consider f(x): 5x Find its inverse if it exists. -

A:

Q: Show that f and g are inverse functions (a) analytically and (b) graphically            f(x) = 16 −…

A:

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

A:

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 of f.

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

Q: 30. Find the inverse function of f(x) = -x² + 8x – 14 if x < 4. Find the domain of this inverse…

A:

Q: Find the inverse function of the function f(x) = 2x5 on the domain x > 0.

A:

Q: Find the inverse of the function on the given domain. f (x) = (x – 11)2, [11, )

A:

Q: Find the inverse function of f(x) F(x)= 3x+1

A: Inverse of a function can be found by replacing x with y and vice versa in the definition of the…

Q: calculate the value of k, when the inverse function of y = 3 ^ x is y = k × ln (x).

A: To finding the inverse we use the logarithmic properties

Q: Find the inverse function of f.

A:

Q: Find the inverse function of f. f(x) = 4 - x2, x ≥ 0

A: Given f(x) = 4 - x2, x ≥ 0

Q: Show that f and g are inverse functions (a) analytically and (b) graphically               f(x) = 5x…

A: Given:fx=5x+1gx=x-15Inverse function: Two function fx and gx are inverses of each other if…

Q: Find the inverse of the function on the given domain. f(x)=(x−10)2 , [10,∞)

A:

Q: Identify the inverse function for g (x)= V2x-2+1.

A:

Q: Find the inverse function f-1(x) if f(x) =x +5.

A:

Q: What is the inverse function of f(x)= 5x+1 and g(x)= x-1?

A: Given the functions:

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

A: Given,          fx=x-182  , [18,∞)

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

A:

Q: Show that f and g are inverse functions (a) analytically and (b) graphically

A: Given: fx=1−x3,  gx=1−x3 Formula: f and g are inverse functions if f∘g(x)=g∘f(x)

Q: Find the domain of the function: h(x) = ln x2

A: h(x)=ln x2

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

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

Q: Show that f and g are inverse functions (a) analytically and (b) graphically              f(x) = 3 −…

A:

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 of the function f(x)=4x^2-9 with domain x less than or equal to 0. f^-1(x)=

A: We have to find inverse of f(x)  in given interval .f(x) and interval is given by:

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

A:

Q: Show that f and g are inverse functions (a) analytically and (b) graphically           f(x) = x3 ,…

A: Given: fx=x3 gx=x3   In order to show that fx and gx are inverse of each other, then, fgx=gfx=x.…

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

A:

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

A:

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

A:

Q: Show that the functions are inverse functions of each other.                                  f(x) =…

A: Given: f(x)=2x3−1g(x)=x+123

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 that f and g are inverse functions algebraically. x3 (x) = , g(x) - V9x f(g(x)) = g(f(x))

A:

Q: Find the inverse function of f. 8x +4 f(x) 1- 5x f(x) =|

A: Solve for the inverse of the function

Q: 1- Vã y = x2-4x2 + 16V, x24 エ-2

A:

Q: Find the inverse of the function. h(x) = 2x h-¹(x) =

A: Let, h(x)=y=2x

Q: . Let f (x) = x* + 3x – 2, and let g(x) denote the inverse of f. Then g'(2) is equal to:

A:

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

A:

Q: 7. Find the inverse of the function f: f(x) = In (x)² – 4, x2 0, using 4 steps

A:

Q: Find the inverse function of f(x) = 12 + x. f-1(z) =

A:

Q: Consider the function:  f(x) = 4x  and find its inverse.

A: Given function:

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.