Question

Which is the inverse of the function f(x) = 4x − 9?

y = 4(x + 9)

Answer 1

The inverse of the function f(x) = 4x − 9 is found by switching x and y and solving for y, resulting in the inverse function f−1(x) = (x + 9) / 4.

Step-by-step explanation:

To find the inverse of the function f(x) = 4x − 9, you need to switch the roles of x and y and then solve for y to get the new function. Here are the steps:

1. Replace f(x) with y: y = 4x − 9.
2. Switch x and y: x = 4y − 9.
3. Solve for y: Add 9 to both sides to get x + 9 = 4y, and then divide both sides by 4 to isolate y, resulting in y = (x + 9) / 4.

The inverse function is f−1(x) = (x + 9) / 4. Note that y = 4(x + 9) is not the correct inverse because it does not undo the operation performed by f(x).

Answer 2

The inverse is 1/4x + 9/4

Step-by-step explanation:

f(x) = 4x − 9

y = 4x -9

Exchange x and y

x = 4y -9

Solve for y

Add x to each side

x+9 = 4y

Divide by 4

1/4x + 9/4 = y

The inverse is 1/4x + 9/4