### Home > CCA > Chapter 11 > Lesson 11.2.2 > Problem11-54

11-54.

For the function $f(x)=7x−2$:

1. Find the inverse function.

Write down the steps for the function. Reverse the order.
Write the new steps using algebra and inverse notation.

The steps for the original function are:
1) Multiply by $7$.
2) Subtract $2$.

$f^{-1}(x)=\frac{x+2}{7}$

2. Show that your inverse function is correct. Choose an input number for the function and calculate the output. Use this output as the input for the inverse function. Is your final output the same as your original input?

Substitute a number for $x$ in $f(x)$, then simplify.
Then substitute your answer from $f(x)$ into the inverse function, then simplify.
If your answer for the inverse function is equal to the value you substituted for $x$ in $f(x)$, your inverse function is correct.