Question

Let f(x) = 2x + 2. Solve f−1(x) when x = 4.

a. 1
b.3
c. 4
d.10

Answer 1

Hi,
Answer a:


`f(x)=2x+2=y\\ y=2x+2\\ x=2y+2\\ x-2=2y\\ y= (x-2)/(2) \\ f^(-1)(x)= (x-2)/(2) \\ f^(-1)(4)= (4-2)/(2)= (2)/(2)=1 \\`

Answer 2

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

A is correct

Explanation:

Given function: f(x)=2x+2

First we will find the inverse of f(x)

f(x)=2x+2

Set f(x)=y, y=2x+2

Switch x and y , x=2y+2

Solve for y to get inverse of f(x)

[yex]y=\dfrac{x-2}{2}[/tex]

Thus,
`f^(-1)(x)=(x-2)/(2)`

Now, we find the value of inverse function at x=4

Put x=4 into inverse function.

`f^(-1)(4)=(4-2)/(2)`

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

Hence, The value of inverse function at x=4 is 1