If the function is one-to-one, find its inverse. If not, write ʺnot one-to-one.ʺ
-$$f ( x ) = ( x + 8 ) ^ { 2 }$$
A) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 8 }$
B) $f ^ { - 1 } ( x ) = \sqrt { x } - 8$
C) not a one-to-one
D) $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x - 8 } }$

Question

Quizplus · Accepted Answer

The function $f(x) = (x + 8)^2$ is not one-to-one because for any given y-value (output), there are two x-values (inputs) that can produce the same output, except for the vertex point. This violates the definition of a one-to-one function, where each x-value has a unique y-value.

If the Function Is One-To-One, Find Its Inverse f(x)=(x+8)2f ( x ) = ( x + 8 ) ^ { 2 }f(x)=(x+8)2

If the Function Is One-To-One, Find Its Inverse $f ( x ) = ( x + 8 ) ^ { 2 }$