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.

Printable View

- Jul 3rd 2006, 10:13 AMkwtolleyfunction defined
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.

- Jul 3rd 2006, 10:52 AMSoltras
$\displaystyle f^{-1}(x)$ 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 $\displaystyle f^{-1}(x) = \frac{x+4}{5} = \frac{1}{5}x + \frac{4}{5}$. - Jul 4th 2006, 12:56 AMkwtolleyanswer
I see now where I was wrong. thanks for checking my answer.