Solve the problem.
-$$f ( x ) = ( x + 11 ) ^ { 2 } - 3 ( x \geq - 11 )$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 3 } - 11 , \mathrm { x } \geq - 3$
B) $f ^ { - 1 } ( x ) = \sqrt { x - 3 } + 11 , x \geq 3$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 3 \mathrm { x } ^ { 2 } + 11 , \mathrm { x } \geq 0$
D) $f ^ { - 1 } ( x ) = \sqrt { x + 11 } + 3 , x \geq - 11$

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 $y = (x + 11)^2 - 3$, we swap to get $x = (y + 11)^2 - 3$, and solve for $y$. Simplifying, we get $y = \sqrt{x + 3} - 11$, which matches choice A, with the domain $x \geq -3$ correctly reflecting the range of the original function.

Solve the Problem f(x)=(x+11)2−3(x≥−11)f ( x ) = ( x + 11 ) ^ { 2 } - 3 ( x \geq - 11 )f(x)=(x+11)2−3(x≥−11)

Solve the Problem $f ( x ) = ( x + 11 ) ^ { 2 } - 3 ( x \geq - 11 )$