Let
\[
f(x)=6-x^{2}, \quad x \geq 0
\]
\[
f^{-1}(x)=
\]

Answer

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Answer

Therefore, the inverse function $f^{-1}(x)$ is $f^{-1}(x) = \boxed{2}$.

Steps

Step 1 ：The number $f^{-1}(x)$ is the value of $x$ such that $f(x) = x$. Since the function $f$ is defined for $x \geq 0$, we only need to consider this case.

Step 2 ：If $x \geq 0$ and $f(x) = x$, then $6 - x^2 = x$, which leads to $x^2 + x - 6 = 0$. This equation factors as $(x - 2)(x + 3) = 0$, so $x = 2$ or $x = -3$. But $x = -3$ does not satisfy $x \geq 0$, so the solution is $x = 2$, which means $f^{-1}(x) = 2$.

Step 3 ：Therefore, the inverse function $f^{-1}(x)$ is $f^{-1}(x) = \boxed{2}$.

Let\[f(x)=6-x^{2}, \quad x \geq 0\]\[f^{-1}(x)=\]

Answer

Popular Problems

Let
\[
f(x)=6-x^{2}, \quad x \geq 0
\]
\[
f^{-1}(x)=
\]