Solve the problem.
-$$f ( x ) = \sqrt { x } - 3$$
A) $f ^ { - 1 } ( x ) = - ( x + 3 ) ^ { 2 } , x \geq - 3$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 3 , \mathrm { x } \geq - 3$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } + 3 ) ^ { 2 } , \mathrm { x } \geq - 3$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } - 3 ) ^ { 2 } , \mathrm { x } \geq - 3$

Question

Quizplus · Accepted Answer

To find the inverse function, we need to solve for $x$ in terms of $f(x)$. Starting with $f(x)=\sqrt{x}-3$, we can first add 3 to both sides, then square both sides to get rid of the square root: $$f(x)+3=\sqrt{x} \implies (f(x)+3)^2=x.$$ Therefore, the inverse function is $f^{-1}(x)=(x+3)^2$, and the answer is choice C.

Solve the Problem f(x)=x−3f ( x ) = \sqrt { x } - 3f(x)=x​−3

Solve the Problem $f ( x ) = \sqrt { x } - 3$