Consider f(x)= 6x and g (x) =  x                                                                    6    Need to find  f(g(x)) and   g(f(x))        and also determine whether the given pair of functions f and g is inverses of each other.

Q: Identify the invariant points of f(x)=4x+2 and it's inverse. Justify your solution.

A: Explanation of the solution is given below...

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

A:

Q: 10. Determine whether g(x) = 3x – 6 and f(x)= x+2 are inverse functions. 3

A: we have to determine whether g(x)=3x-6  and f(x)=13x+2 are inverse functions.

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

A:

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: Find a formula for the inverse of the function. f(x) = 8 – x², x > 0 f-1(x) = %3D

A:

Q: If f(x) find the inverse function. 9x – 2 f1(x) =

A:

Q: Verify if f (x) = x-3 and g(x) = 5x 3 are inverses.

A: They are inverse function

Q: 6-10x Find the inverse function for f(x) = 8x+7 and verify your inverse by computing both of…

A:

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

A:

Q: Find the inverse of f(x)=-V4.x+1.

A:

Q: 17. Determine whether f(x) = 5x - 3 and g(x) = 2 +3 are inverse functions.

A:

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

A:

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

A: Given,          fx=x-182  , [18,∞)

Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: f(x)=x3-6x2+12x

Q: Find the inverse of the function y = In (x - 2). %3D

A: y = f(x) = ln (x-2) ey = x-2 x = 2 + ey x = f-1(y) = 2 + ey

Q: 6-10x Find the inverse function for f(x) 8x+7 and verify your inverse by computing both of…

A:

Q: Use the Product Rule to find the derivative of the function. g(x) = (x2 - 2x + 5)(x³ - 6) g'(x) =

A:

Q: The inverse function of f(x) = 4x + 2 is %3D f-1(2) =

A:

Q: How do I find the inverse function of f(x) = 1/x+4?

A: Given function,  Let y = f(x)

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

A:

Q: Find the inverse of g (x) = ÷x +. g1 (x) = *x -

A:

Q: Example 3: Find the inverse of y=x+1, expressed as a function of x.

A: For finding the inverse function, we will replace x with y and y with x as follows

Q: f(x) = 2x + 3 - g(x) = 5x +7

A:

Q: Determine where the two functions g(x)=(x-5)^3 and h(x)=^3 square root of x+5 are inverses.

A:

Q: Find the inverse of f (x) = x +b, where b is constant. How is the graph of f related to the graph f.

A: Inverse of functions return its original value for which a function gave output

Q: What is the inverse of f(x) = x+1?

A:

Q: Verify graphically that the functions f(x) = x2 (x ≥ 0) and g(x) = √x are inversefunctions of each…

A: fx=x2  x≥0  &  gx=x. The graph is,

Q: Find the inverse of f(x) = x2 - 1 if x ≥ 0. Graph f and f -1 in the same rectangular coordinate…

A: Given: fx=y=x2-1 for finding inverse of given function, first we find x in terms of y then replace x…

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

A: Given: f(x)=2x3−1g(x)=x+123

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

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

Q: 7) Find the inverse of the function g(x) = x² + 2x,[-1,0)

A: Simply replace the x by y and f(x) to x and solve the new equation for 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: Find the inverse function of f.

A:

Q: Find the inverse function of f.

A: Let the two functions P and Q be inverse of each other then this implies that Q(y)=x if and only if…

Q: are f(x)=x+2/x-2 and g(x)=2x+2/x-1 inverses of each-other?

A:

Q: Does the function f (x) = x2 - 3x have an inverse?

A: fx=x2-3x

Q: Verify graphically that the functions f(x) = 2x − 3 and g(x) = 12 (x + 3) are inversefunctions of…

A: Inverse function: If two function f(x) and g(x) are symmetric about the line y = x then f(x) and…

Q: Given f (æ) = 3x + 2 and g (æ) = x - 1. Find f (g (x)). 2. Find g (f (x)). 3. Are the functions…

A: The functions are given by f(x) = 3x+2 and g(x) = 13x-23 To evaluate : 1. fgx2. gfx3. Are the…

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

A:

Q: Find the first and second derivatives of the function. g(x) = -4x3 + 11x2 + 6x - 51 g'(x) g"(x)

A:

Q: b) Verify that f(x) = 5x – 1 and g(x) = x+1 are inverse functions. 5 %3D

A:

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: Let f (x) = x³ – 5x² – 8 and let g be the inverse of f ( -

A: Given,   And

Q: find the inverse of a function f(x) = (2x+3)/(x+2)

A:

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

A:

Q: verify the inverse function theorem of y=4x^2+4x+9

A:

Q: Identify the invariant points of f(x)=4x+2 and its inverse.  Justify your solution

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.