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 does not pass the horizontal line test). For any given y-value (greater than 5), there are two x-values (one positive and one negative) that will produce that y-value, making it impossible to define a unique inverse.

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 $f ( x ) = x ^ { 2 } + 5$