Answer
See proof
Work Step by Step
We are given the functions:
$f(x)=7x+1$
$g(x)=\dfrac{x-1}{7}$
a) Verify that the two functions are inverse functions.
Determine $f\circ g$ and $g\circ f$:
$(f\circ g)(x)=f(g(x))=f\left(\dfrac{x-1}{7}\right)=7\left(\dfrac{x-1}{7}\right)+1=x-1+1=x$
$(g\circ f)(x)=g(f(x))=g(7x+1)=\dfrac{7x+1-1}{7}=\dfrac{7x}{7}=x$
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.
