Problem

$f(x)=\sqrt{x}+7$. Find the inverse of $f(x)$ and its domain.

Answer

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Answer

\(f^{-1}(x) = (x - 7)^2\) and its domain is \([7, \infty)\)

Steps

Step 1 ：Swap x and y: \(x = \sqrt{y} + 7\)

Step 2 ：Solve for y: \(y = (x - 7)^2\)

Step 3 ：\(f^{-1}(x) = (x - 7)^2\) and its domain is \([7, \infty)\)

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