Determine whether the given function is one-to-one. If it is one-to-one, find its inverse function.
-$$f ( x ) = 6 x ^ { 2 }$$
A) $f ^ { - 1 } ( x ) = \frac { 1 } { 6 x ^ { 2 } }$
B) $f ^ { - 1 } ( x ) = \frac { 6 } { x ^ { 2 } }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 6 \sqrt { \mathrm { x } }$
D)not a one-to-one function

Question

Quizplus · Accepted Answer

The function $f(x) = 6x^2$ is not one-to-one because for any given y-value, there can be two different x-values (one positive and one negative) that produce the same output. This violates the definition of a one-to-one function, where each x-value must map to a unique y-value.

Determine Whether the Given Function Is One-To-One f(x)=6x2f ( x ) = 6 x ^ { 2 }f(x)=6x2

Determine Whether the Given Function Is One-To-One $f ( x ) = 6 x ^ { 2 }$