Question

Write the inverse function for the function, ƒ(x) = 1/2x + 4. Then, find the value of ƒ -1(4). Type your answers in the box. ƒ -1(x) = a0 x a1 a2 ƒ -1(4) = a3

Answer 1

ƒ(x) = 1/2x + 4

inverse

x = 1/2 y + 4
2x = y + 8
y = 2x - 8
so inverse f-1(x) = 2x - 8

ƒ -1(4) = 2(4) - 8 = 0

answer

ƒ -1(x) = 2x - 8
ƒ -1(4) = 0

Answer 2

`f^(-1)(x) = 2x - 8\\ f^(-1)(4) = 0`

Explanation:

To find an inverse function, we need to think the function as an equality x = 1/2y + 4 that we have to resolve for the y.

First, let's subtract 4 from both sides.

x - 4 = 1/2y + 4 - 4

x - 4 = 1/2y

Now we multiply by 2 on both sides.

(x-4)*2 = 1/2y*2

2*x-8 = y

Therefore, the inverse function is

`f^(-1)(x)=2x-8`

To find out
`f^(-1)(4)`, we need to replace the x of the function with a 4:

`f^(-1)(4)` = 2*4 - 8 = 8 - 8 = 0

`f^(-1)(4)`= 0