Question

f (x) = 8x + 7. Find the inverse of f(x).
O A. f¹(x) = 7 - 8x
O B. f¹(x) = 8x - 7
O c. f¹(x) = 278
x-8
O D. f-¹(x) = 2=7
8

Answer 1

Answer:

${f}^{ - 1} (x) = \frac{1}{8} x + \frac{7}{8}$

What are inverse functions?

Inverse functions undo the operation of the original function. That is, if x undergoes function f to become f(x), then the inverse function (denoted by f⁻¹) reverse what function f does. Thus, the inverse function of f changes f(x) back into x.

Obtaining the expression for inverse functions

The inverse of a function can be found in 3 main steps, which is to first let y= f(x), then make x the subject of formula before replacing x with f⁻¹(x) and y with x.

Let's apply the above steps to solve the question!

Given: f(x)= 8x +7

Step 1: Let y= f(x).

y= 8x +7

Step 2: Make x the subject of formula.

Start by subtracting 7 from both sides:

8x= y -7

Divide both sides by 8:

$x = \frac{1}{8} y + \frac{7}{8}$

Step 3: Replace x with f⁻¹(x) and y with x.

${f}^{ - 1} (x) = \frac{1}{8} x + \frac{7}{8}$

Additional

To learn more about inverse functions, check out: https://brainly.com/question/19755382