Determine whether the function has an inverse function.If it does, find the inverse function. $$f ( x ) = x ^ { 2 } + 5$$
A) No inverse function exists.
B) $f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$
C) $f ^ { - 1 } ( x ) = \sqrt { x } - 5$
D) $f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 6$
E) $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$

Question

Quizplus · Accepted Answer

The function $f(x) = x^2 + 5$ does not have an inverse function because it is not one-to-one (it fails the horizontal line test). For any given y-value (greater than 5), there are two x-values (one positive and one negative) that map to it, which means it cannot be inverted in its current form without restricting the domain.

Determine Whether the Function Has an Inverse Function f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5

Determine Whether the Function Has an Inverse Function $f ( x ) = x ^ { 2 } + 5$