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

Question

Quizplus · Accepted Answer

To find the inverse function $f^{-1}(x)$, we swap $x$ and $y$ in the original function and solve for $y$. The original function is $f(x) = (x - 11)^2$ for $x \geq 11$. Swapping $x$ and $y$, we get $x = (y - 11)^2$. Taking the square root of both sides gives $y = \sqrt{x} + 11$, and since the original function is defined for $x \geq 11$, the inverse function will be defined for $x \geq 0$, making the correct answer $\sqrt{x} + 11, x \geq 0$.

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

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