Question

write the inverse of $f(x) = 5x - 4$?
$f^{-1}(x) = \square \square$

Explanation:

Step1: Replace \( f(x) \) with \( y \)

We start with the function \( f(x) = 5x - 4 \). Replace \( f(x) \) with \( y \), so we have \( y = 5x - 4 \).

Step2: Swap \( x \) and \( y \)

To find the inverse, we swap the roles of \( x \) and \( y \). This gives us \( x = 5y - 4 \).

Step3: Solve for \( y \)

First, add 4 to both sides of the equation: \( x + 4 = 5y \). Then, divide both sides by 5 to isolate \( y \): \( y=\frac{x + 4}{5}\). We can also write this as \( y=\frac{1}{5}x+\frac{4}{5}\).

Step4: Replace \( y \) with \( f^{-1}(x) \)

Now, replace \( y \) with \( f^{-1}(x) \) to get the inverse function. So \( f^{-1}(x)=\frac{x + 4}{5}\) (or \( f^{-1}(x)=\frac{1}{5}x+\frac{4}{5}\)).

Answer:

\( f^{-1}(x)=\frac{x + 4}{5} \) (or \( f^{-1}(x)=\frac{1}{5}x+\frac{4}{5} \))