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What is the inverse of f(x) = 2x2 –4?

User Josh Gafni
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Answer:

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) }

User LightCZ
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