Which function is the inverse of f (x) = 4x - 3/4?

Question

A. f^-1(x) = 1/4x + 3/16

B. f^-1(x) = -1/4x + 3

C. f^-1(x) = 1/4x + 3

D. f^-1(x) = -1/4x + 3/16

These are the options. Please explain how you got the answer.

Answer 1

Here are the steps to solve this problem.

 

f(x) = 4x - 3/4

Change f(x) to y

 

y = 4x - 3/4

Switch the x and y variables

 

x = 4y - 3/4

Now solve for y. Add 3/4 to both sides

 

x + 3/4 = 4y

Divide by 4

 

1/4x +3/16 = y

Change y to inverse function notation

 

f^-1(x) = 1/4 x + 3/16