Question

Help me please!

Consider the function f(x) = V2x – 4. Iff-'(x) is the inverse function of f(x), find
f-16)

Answer 1

`f^(-1)(6) = 50`

Explanation:

Given

`f(x) = √(2x) - 4`

Required

Find
`f^(-1)(6)`

First, we calculate the inverse function

`f(x) = √(2x) - 4`

Express f(x) as y

`y = √(2x) - 4`

Swap the positions of x and y

`x = √(2y) - 4`

Solve for y: Add 4 to both sides

`4 + x = √(2y) - 4+4`

`4 + x = √(2y)`

Square both sides

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

Divide both sides by 2

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

Express y as an inverse function

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

Next, solve for:
`f^(-1)(6)`

Substitute 6 for x

`f^(-1)(6) = ((4 + 6)^2)/(2)`

`f^(-1)(6) = ((10)^2)/(2)`

`f^(-1)(6) = (100)/(2)`

`f^(-1)(6) = 50`