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

Answer

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Answer

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

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 $f^{- 1} (x) = 2$ .

Letf(x)=6−x2,x≥0f−1(x)=

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Popular Problems

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