Find the inverse of the function.
-$$f ( x ) = ( x - 5 ) ^ { 2 } , x \geq 5$$
A) Not a one-to-one function
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 5 } , \mathrm { x } \geq 5$
C) $f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \sqrt { \mathrm { x } } + 5 , \mathrm { x } \geq 0$

Question

Quizplus · Accepted Answer

To find the inverse of the function $f(x) = (x - 5)^2, x \geq 5$, we swap $x$ and $y$ and solve for $y$. So, we have $x = (y - 5)^2$. Taking the square root of both sides gives $\sqrt{x} = y - 5$, which leads to $y = \sqrt{x} + 5$. Since the original function is defined for $x \geq 5$, its inverse will be defined for $x \geq 0$ (since $(5 - 5)^2 = 0$). Therefore, the correct inverse function is $f^{-1}(x) = \sqrt{x} + 5, x \geq 0$.

Find the Inverse of the Function f(x)=(x−5)2,x≥5f ( x ) = ( x - 5 ) ^ { 2 } , x \geq 5f(x)=(x−5)2,x≥5

Find the Inverse of the Function $f ( x ) = ( x - 5 ) ^ { 2 } , x \geq 5$