Question

what is the inverse function to f(x) = (6-8x)/(3-3x)

Write the expression as an equivalent expression in the form x^n.
1/(x^7)

Answer 1

\(y=\frac{6-8x}{3-3x}\iff y(3-3x)=6-8x\iff 3y-3xy=6-8x \iff\\-3xy+8x=-3y+6\iff x(-3y+8)=-3y+6 \iff x=\frac{-3y+6}{-3y+8}\)
so

\(f^{-1}(x)=\frac{6-3x}{8-3x}\)