The image you provided shows a student's work proving that two functions $f(x) = 3x - 7$ and $g(x) = \frac{x + 7}{3}$ are inverses.

The student is performing a process to check if the two functions are inverses by verifying two conditions:

1. $f(g(x)) = x$
2. $g(f(x)) = x$

The student has worked through $f(g(x)) = x$, but the student needs to check the other condition, $g(f(x)) = x$, to complete the proof.

Thus, the correct statement from the multiple-choice options is:

• The student must also show $g(f(x)) = x$.

Would you like further explanation on how to verify that two functions are inverses?

Related Questions:

1. How do you compute $g(f(x))$ for these functions?
2. Why is it important to check both $f(g(x)) = x$ and $g(f(x)) = x$?
3. What does it mean for two functions to be inverses of each other?
4. How can you use derivatives to check if two functions are inverses?
5. What is the graphical relationship between inverse functions?

Tip:

When proving that two functions are inverses, always remember to verify both conditions: $f(g(x)) = x$ and $g(f(x)) = x$. This ensures that the functions truly undo each other.