Find the inverse function of the function \( f(x)=5 x-4 \) Answer \( f^{-1}(x)=\frac{x+4}{5} \) \( f^{-1}(x)=\frac{x-4}{5} \)

Let's dive into how the function \( f(x) = 5x - 4 \) reverses its steps! To find the inverse, we want to swap \( x \) and \( y \) in the original equation and solve for \( y \). So starting from \( y = 5x - 4 \), we switch to \( x = 5y - 4 \). Rearranging gives us \( 5y = x + 4 \) and thus \( y = \frac{x + 4}{5} \). So, you nailed it with \( f^{-1}(x) = \frac{x + 4}{5} \)! Similarly, in the world of functions, understanding inverses is like dancing in reverse! Any time you have a linear function, its inverse will also be linear. Just make sure to flip those variables, keep track of your arithmetic, and you'll be successfully finding inverses in no time! Always double-check by composing \( f(f^{-1}(x)) \) to ensure that you return to \( x \) as expected. Keep practicing, and soon it will be second nature!