1

Problem

Find the inverse of a linear function f(x) = 4x + 5.

2

Step

Given the linear function

f(x) = 4x + 5

3

Hint

To find the inverse of a linear function, we’ll swap the x and y variables and solve for y.

4

Step

let’s replace f(x) with y:

y = 4x + 5

5

Step

Let’s switch the x and y variables and move the constant term to the left side:

x = 4y + 5

x - 5 = 4y

6

Step

Divide both sides by 4:

\$(x - 5) / 4 = (4y) / 4\$

\$y = (x - 5) / 4\$

7

Solution

Therefore, the inverse of the linear function f(x) = 4x + 5 is: \$f^(-1)(x) = (x - 5) / 4\$.

8

Sumup

Please summarize steps

Choices

9

Choice-A

This option has an incorrect intercept; it should be -5 instead of +5 for the inverse function

Wrong \$f^(-1)(x) = (x + 5) / 4\$

10

Choice-B

This option has a different slope and an incorrect intercept, making it the wrong choice for the inverse function

Wrong \$f^(-1)(x) = (x - 4) / 5\$

11

Choice-C

This option correctly represents the inverse function with the right slope and intercept

Correct \$f^(-1)(x) = (x - 5) / 4\$

12

Choice-D

This option suggests adding 4 and dividing by 5, resulting in an incorrect slope and intercept

Wrong \$f^(-1)(x) = (x + 4) / 5\$

13

Answer

Option

C

14

Sumup

Please summarize choices