Question

Which of the following graphs is the inverse of the

function f(x)=√x+4-2
-8
-2
-6
6
4
-2-
0
-2
2
4
2-
0
-2
4
4
2
4

Answer 1

The graph of the inverse of the function
`\text{f(x)} = √(x + 4) - 2` is added as an attachment

How to determine the graph that represents the inverse function

From the question, we have the following parameters that can be used in our computation:

`\text{f(x)} = √(x + 4) - 2`

Represent the function as an equation

So, we have

`\text{y} = √(x + 4) - 2`

Swap the variables x and y

This gives

`\text{x} = √(y + 4) - 2`

So, we have

`\text{x + 2} = √(y + 4)`

Square both sides

`(x + 2)^2 = y + 4`

Make the variable y the subject

`y = (x + 2)^2 - 4`

Express as an inverse function

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

The graph of the inverse function is added as an attachment