Question

solve $f(x)=30$ for the function $f(x)=7x + 9$. 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 \( f(x) = 30 \)

Set \( 7x + 9 = 30 \). Subtract 9 from both sides: \( 7x = 30 - 9 = 21 \). Then divide by 7: \( x = \frac{21}{7} = 3 \).

Step2: Find the inverse function

Let \( y = 7x + 9 \). Swap \( x \) and \( y \): \( x = 7y + 9 \). Solve for \( y \): Subtract 9: \( x - 9 = 7y \), then divide by 7: \( y = \frac{x - 9}{7} \). So \( f^{-1}(x) = \frac{x - 9}{7} \).

Answer:

• \( x = 3 \)
• \( f^{-1}(x) = \frac{x - 9}{7} \)