Question

f(x) = 5/(7x-8) What is the inverse of this function?

Answer 1

$f(x)=\dfrac{5}{7x-8}\\ y=\dfrac{5}{7x-8}\\ 7x-8=\dfrac{5}{y}\\ 7x=\dfrac{5}{y}+8\\ x=\dfrac{5}{7y}+\dfrac{8}{7}\\ \boxed{f^{-1}(x)=\dfrac{5}{7x}+\dfrac{8}{7}}$

Answer 2

$f(x)=\dfrac{5}{7x-8}\\\\y=\dfrac{5}{7x-8}\iff\dfrac{1}{y}=\dfrac{7x-8}{5}\ \ \ |multiply\ both\ sides\ by\ 5\\\\\dfrac{5}{y}=7x-8\ \ \ |add\ 8\ to\ both\ sides\\\\7x=\dfrac{5}{y}+8\\\\7x=\dfrac{5}{y}+\dfrac{8y}{y}\\\\7x=\dfrac{5+8y}{y}\ \ \ \ |divide\ both\ sides\ by\ 7\\\\x=\dfrac{5+8y}{7y}\\\\Answer:\boxed{f^{-1}(x)=\dfrac{5+8x}{7x}\ other\ form\ f^{-1}(x)=\dfrac{5}{7x}+\dfrac{8}{7}}$