Find the inverse function of f. f(x) = 2 − x2, x ≥ 0 f −1(x) = , x ≤ 2

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Mathematics

Description

Find the inverse function of f.

f(x) = 2 − x2,    x ≥ 0
f −1(x) = 

 ,    x ≤ 2

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Explanation & Answer

Hello!

To find the inverse function, f^(-1)(y), we have to solve for x the equation

y = f(x) = 2 - x^2.

It is simple:

x^2 = 2 - y,

x = f^(-1)(y) = sqrt(2-y).

Here y must be <=-2 and we choose +sqrt(2-y), not -sqrt(2-y), because it is given that x>=0.

Please ask if anything is unclear.


Anonymous
Just what I was looking for! Super helpful.

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