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

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

 ,    x ≤ 2

Oct 19th, 2017


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.
Jul 1st, 2015

answer is incorrect

Jul 2nd, 2015

Of course y<=2, not -2. But the formula for f^(-1) is correct, I see no error.

maybe you want y to be replaced by x,

f^(-1)(x) = sqrt(2-x)  ?

sqrt is for square root

Jul 2nd, 2015

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