The given problem asks to express the function $h(x) = \frac{1}{x + 7}$ in the form $f(g(x))$, where $g(x) = x + 7$ and we need to find the function $f(x)$.

We know that:

• $h(x) = \frac{1}{x + 7}$
• $g(x) = x + 7$

To express this as $f(g(x))$, substitute $g(x) = x + 7$ into $h(x)$:

$h(x) = \frac{1}{g(x)}$

Thus, the function $f(x)$ should be:

$f(x) = \frac{1}{x}$

So, the answer is: $f(x) = \frac{1}{x}$

Would you like further details or clarification?

Here are 5 related questions to consider:

1. How would you solve this if $g(x)$ was a different function?
2. How does the composition of functions work in general?
3. What happens if you reverse the functions, i.e., $g(f(x))$?
4. How can you check your answer in this problem?
5. Can you provide another example of a function composition?

Tip: When dealing with compositions, always substitute one function into the other and simplify!