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:

$f(x)=2x+2=y\\ y=2x+2\\ x=2y+2\\ x-2=2y\\ y= \dfrac{x-2}{2} \\ f^{-1}(x)= \dfrac{x-2}{2} \\ f^{-1}(4)= \dfrac{4-2}{2}= \dfrac{2}{2}=1$

Answer 2

Answer:

$f^{-1}(4)=1$

A is correct

Step-by-step 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, $f^{-1}(x)=\dfrac{x-2}{2}$

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

Put x=4 into inverse function.

$f^{-1}(4)=\dfrac{4-2}{2}$

$f^{-1}(4)=1$

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