Question

solve $f(x) = 18$ for the function $f(x) = 5x - 7$. then, find an expression for the inverse of $f(x)$. use the keypad to enter your answers in the boxes. - $x = \square$ - $f^{-1}(x) = \square$

Explanation:

Step1: Solve \( f(x) = 18 \)

Set \( 5x - 7 = 18 \). Add 7 to both sides: \( 5x = 18 + 7 = 25 \). Then divide by 5: \( x = \frac{25}{5} = 5 \).

Step2: Find the inverse function

Start with \( y = 5x - 7 \). Swap \( x \) and \( y \): \( x = 5y - 7 \). Solve for \( y \): Add 7 to both sides: \( x + 7 = 5y \). Divide by 5: \( y = \frac{x + 7}{5} \), so \( f^{-1}(x) = \frac{x + 7}{5} \).

Answer:

\( x = 5 \)
\( f^{-1}(x) = \frac{x + 7}{5} \)