Determine whether the function has an inverse function. If it does, find the inverse function.
$g ( x ) = \frac { x } { 4 }$
A) $g ^ { - 1 } ( x ) = - 4 x$
B) $g ^ { - 1 } ( x ) = 4 x$
C) $g ^ { - 1 } ( x ) = \frac { 4 } { x }$
D)$g ^ { - 1 } ( x ) = - \frac { x } { 4 }$
E) No inverse

Question

Determine whether the function has an inverse function. If it does, find the inverse function. 
$g ( x ) = \frac { x } { 4 }$
A) $g ^ { - 1 } ( x ) = - 4 x$
B) $g ^ { - 1 } ( x ) = 4 x$
C) $g ^ { - 1 } ( x ) = \frac { 4 } { x }$
D)$g ^ { - 1 } ( x ) = - \frac { x } { 4 }$
E) No inverse

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = \frac{x}{4}$, swapping gives $x = \frac{y}{4}$, which leads to $y = 4x$. This shows $g^{-1}(x) = 4x$.

Determine Whether the Function Has an Inverse Function g(x)=x4g ( x ) = \frac { x } { 4 }g(x)=4x​

Determine Whether the Function Has an Inverse Function $g ( x ) = \frac { x } { 4 }$