Question

Find the inverse of the quadratic function $f$.
$f\left(x\right)=-x^2+2,x>=0$

• A. $\sqrt{(2+x)}$
• B. $(2-x)$
• C. $\sqrt{(2+x^2)}$
• D. $\sqrt{(2-x)}$

Answer 1

The correct option is D $\sqrt{(2-x)}$

Let $y=f\left(x\right)=-x^2+2$ and now solve for $x$ to find the inverse of the given function.

$\Rightarrow y=x^2+2$

$\Rightarrow -x^2=y-2$

$\Rightarrow x^2=2-y$

$\Rightarrow x=\pm \sqrt{2-y}$

Since it is given that $x>=0$, therefore,

$x=\sqrt{2-y}$

Therefore, the inverse of the function in terms of $x$ is $\sqrt{2-x}$.