Find the inverse function of $f ( x ) = \sqrt { x + 5 } , x \geq - 5$ .
A) $f ^ { - 1 } ( x ) = x ^ { 2 } - 5 , x \geq 0$
B) $f ^ { - 1 } ( x ) = x ^ { 2 } - 25 , x \geq 0$
C) $f ^ { - 1 } ( x ) = ( x - 25 ) ^ { 2 }$
D) $f ^ { - 1 } ( x ) = ( x - 5 ) ^ { 2 }$
E)The function does not have an inverse.

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = \sqrt{x + 5}$, we swap to get $x = \sqrt{y + 5}$. Squaring both sides gives $x^2 = y + 5$, and solving for $y$ gives $y = x^2 - 5$. The domain of the original function restricts $x \geq -5$, which translates to the range $x \geq 0$ for the inverse function, making $f^{-1}(x) = x^2 - 5, x \geq 0$ correct.

Find the Inverse Function Of f(x)=x+5,x≥−5f ( x ) = \sqrt { x + 5 } , x \geq - 5f(x)=x+5​,x≥−5

Find the Inverse Function Of $f ( x ) = \sqrt { x + 5 } , x \geq - 5$