Given:
[tex]\begin{gathered} f(x)=3x+1_{} \\ g(x)=\frac{x-1}{3} \end{gathered}[/tex]
To check the given functions are inverses of each other,
[tex]\begin{gathered} To\text{ prove: }f\mleft(g\mleft(x\mright)\mright)=x\text{ and g(f(x)=x} \\ f(g(x))=f(\frac{x-1}{3}) \\ =3(\frac{x-1}{3})+1 \\ =x-1+1 \\ =x \end{gathered}[/tex]
And,
[tex]\begin{gathered} g(f(x))=g(3x+1) \\ =\frac{(3x+1)-1}{3} \\ =\frac{3x+1-1}{3} \\ =\frac{3x}{3} \\ =x \end{gathered}[/tex]
It shows that, the given functions are inverses of each other.
The graph of the function is,
Blue line represents g(x)
Red line represents f(x)
green line represents y=x
