Determine whether the function has an inverse function, If it does, find its inverse function. $f ( x ) = x ^ { 4 }$
A)No, $f$ does not have an inverse function.
B)Yes, $f$ has an inverse function, $y = x ^ { 4 }$
C)Yes, $f$ has an inverse function, $y = - x ^ { - 4 }$
D)Yes, $f$ has an inverse function, $y = x ^ { - 4 }$
E)Yes, $f$ has an inverse function, $y = - x ^ { 4 }$

Question

Quizplus · Accepted Answer

The function $f(x) = x^4$ does not have an inverse function because it is not one-to-one; for any given y-value, there are two x-values (one positive and one negative) that produce the same result when raised to the fourth power, violating the requirement for a function to have an inverse.

Determine Whether the Function Has an Inverse Function, If It f(x)=x4f ( x ) = x ^ { 4 }f(x)=x4

Determine Whether the Function Has an Inverse Function, If It $f ( x ) = x ^ { 4 }$