Question

What is the inverse of f(x) = 2x2 –4?

Answer 1

The inverse of the function is

`{ \underline{f {}^( - 1)(x) = \sqrt{ (x + 4)/(2) } }}`

Explanation:

let the inverse of f(x) be m:

`m = {2x}^(2) - 4`

take 4 to the left hand side ( changes sign to positive ):

`m + 4 = {2x}^(2) \\ (m + 4)/(2) = {x}^(2)`

take a square root on all sides:

`\sqrt{ (m + 4)/(2) } = \sqrt{ {x}^(2) } \\ \\ x = \sqrt{ (m + 4)/(2) }`

substitute x in place of m:

`{f}^( - 1) (x) = \sqrt{ (x + 4)/(2) }`