For the function defined by f(x)=5x-4, find a formula for f^-1(x). My answer is f^-1(x)= 1 divided by 5x-4, is this right. thanks for checking.
$\displaystyle f^{-1}(x)$ doesn't mean $\displaystyle \frac{1}{f(x)}$.
Think of it this way:
If $\displaystyle y = f(x) = 5x-4$ then the inverse function is denoted $\displaystyle f^{-1}(x)$ and is just the expression with the x and y switched, and then solved for y.
Switching y and x, you get:
$\displaystyle x = 5y - 4$.
Isolate the y to get:
$\displaystyle y = \frac{x+4}{5}$
So $\displaystyle f^{-1}(x) = \frac{x+4}{5} = \frac{1}{5}x + \frac{4}{5}$.