Find f - -1 ( x ). $f ( x ) = \sqrt { 5 x } \text { for } x \geq 0$
A) $f ^ { - 1 } ( x ) = 5 x ^ { 2 }$
B) $f ^ { - 1 } ( x ) = \frac { x } { 5 }$
C) $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } } { 5 }$

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 $y = \sqrt{5x}$, we swap to get $x = \sqrt{5y}$. Squaring both sides gives $x^2 = 5y$, and solving for $y$ gives $y = \frac{x^2}{5}$, which corresponds to choice C.

Find F - -1 ( X ) f(x)=5x for x≥0f ( x ) = \sqrt { 5 x } \text { for } x \geq 0f(x)=5x​ for x≥0

Find F - -1 ( X ) $f ( x ) = \sqrt { 5 x } \text { for } x \geq 0$