Find f - -1 ( x ). $f ( x ) = x ^ { 2 } + 7 \text { for } x \geq 0$
A) $f ^ { - 1 } ( x ) = \sqrt { x + 7 }$
B) $f ^ { - 1 } ( x ) = \sqrt { x - 7 }$
C) $f ^ { - 1 } ( x ) = x - 7$

Question

Quizplus · Accepted Answer

To find the inverse function, $f^{-1}(x)$, we swap $x$ and $y$ in the original function and solve for $y$. Starting with $y = x^2 + 7$, we swap to get $x = y^2 + 7$, and solving for $y$ gives $y = \sqrt{x - 7}$, which corresponds to choice B.

Find F - -1 ( X ) f(x)=x2+7 for x≥0f ( x ) = x ^ { 2 } + 7 \text { for } x \geq 0f(x)=x2+7 for x≥0

Find F - -1 ( X ) $f ( x ) = x ^ { 2 } + 7 \text { for } x \geq 0$