what is the inverse of f(x)=1/3x-7 ?

what is the inverse of f(x)=1/3x-7 ?

$y=\frac{1}{3}x-7\\ y+7=\frac{1}{3}x\\ 3(y+7)=x\\ x=3(y+7)$

So the inverse of

$f(x)=\frac{1}{3}x-7\qquad is\\ f(x)=3(x+7)$

See how the inverse is the refletion of the original function about the line y=x  ?

All inverse functions are the reflection of the original function about the line y=x !!