Answer
See proof
Work Step by Step
We are given the functions:
$f(x)=3-4x$
$g(x)=\dfrac{3-x}{4}$
a) Verify that the two functions are inverse functions.
Determine $f\circ g$ and $g\circ f$:
$(f\circ g)(x)=f(g(x))=f\left(\dfrac{3-x}{4}\right)=3-4\left(\dfrac{3-x}{7}\right)=3-(3-x)=3-3+x=x$
$(g\circ f)(x)=g(f(x))=g(3-4x)=\dfrac{3-(3-4x)}{4}=\dfrac{3-3+4x}{4}=\dfrac{4x}{4}=x$
We got:
$(f\circ g)(x)=(g\circ f)(x)=x$,
therefore the two functions are inverse functions.
b) Graph $f$ and $g$ and the line $y=x$.
As the graphs of $f$ and $g$ are symmetric with respect to the line $y=x$, $f$ and $g$ are inverse functions.
