Question

What is the inverse of f(x)=5x-8

Answer 1

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

Explanation:

`f(x)=5x-8\to y=5x-8\\\\\text{change}\ x\ \text{to}\ y\ \text{and vice versa}\\\\x=5y-8\\\\\text{solve for}\ y:\\\\5y-8=x\qquad\text{add 8 to both sides}\\\\5y-8+8=x+8\\\\5y=x+8\qquad\text{divide both sides by 5}\\\\(5y)/(5)=(x)/(5)+(8)/(5)\\\\y=(1)/(5)x+(8)/(5)`