Question

Which function is the inverse of if the domain of f(x) is x ≥ 0?

Answer 1

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Which function is the inverse of

$f(x)=x^2-16$

if the domain of f(x) is x ≥ 0?

The inverse funtion of the given function is given by

$\mathbf{f(x)=\sqrt{x+16}}$

where the domain is x ≥ -16.

Given the function is,

$f(x) =x^2-16$

Let, y = f(x)

$y = x^2-16$

Adding 16 to both sides we get,

$y + 16 = {x}^{2} - 16 + 16$

${x}^{2} = y + 16$

Now, square rooting to both sides we get, since x ≥ 0

$\sqrt{x^2}=\sqrt{y+16}$

$x=\sqrt{y+16}$

$f^{-1}(y)=\sqrt{y+16}$

Hence substituting x in place of y,

$f^{-1}(x)=\sqrt{x+16}$

Above function is the required inverse function where the domain of that is given by, x ≥ -16.

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