Question

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

Answer 1

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

Answer 2

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