f(x)= − 3/1x+6 find the inverse function in slope intercept form mx+b

Question

f(x)=

−31​x+6

Answer 1

Let y=f(x)=31x+6, then 31x=y-6 and x=y/31-6/31.

Let x=g(y)=y/31-6/31, so g(x)=f^-1(x)=x/31-6/31 in the required standard form (m=1/31 and b=-6/31).

We need to prove this to be the inverse function f(f^-1(x))=f^-1(f(x))=x.

Let's prove it:

f(f^-1(x))=31f^-1(x)+6=31(x/31-6/31)+6=x-6+6=x✔️

f^-1(f(x))=f(x)/31-6/31=(31x+6)/31-6/31=x+6/31-6/31=x✔️