Determine whether the given functions are inverses of each other.
-$$f ( x ) = \frac { x + 7 } { 4 } , \quad g ( x ) = 4 x + 7$$
A)Yes
B)No

Question

Quizplus · Accepted Answer

To determine if two functions are inverses of each other, one function must undo the operation of the other. If $f(g(x)) = x$ and $g(f(x)) = x$, then they are inverses. For $f(x) = \frac{x + 7}{4}$ and $g(x) = 4x + 7$, applying $g$ to $f(x)$ gives $g(f(x)) = 4\left(\frac{x + 7}{4}\right) + 7 = x + 7 + 7$, which does not simplify to $x$. Similarly, applying $f$ to $g(x)$ gives $f(g(x)) = \frac{4x + 7 + 7}{4}$, which also does not simplify to $x$. Therefore, they are not inverses of each other.

Determine Whether the Given Functions Are Inverses of Each Other f(x)=x+74,g(x)=4x+7f ( x ) = \frac { x + 7 } { 4 } , \quad g ( x ) = 4 x + 7f(x)=4x+7​,g(x)=4x+7

Determine Whether the Given Functions Are Inverses of Each Other $f ( x ) = \frac { x + 7 } { 4 } , \quad g ( x ) = 4 x + 7$