The given function $h(x) = \sqrt{9x - 5}$ needs to be expressed as a composition of two functions $f$ and $g$, such that $h(x) = f(g(x))$. Here's one way to decompose it:

1. Let $g(x) = 9x - 5$. This function maps $x$ to $9x - 5$.
2. Let $f(x) = \sqrt{x}$. This function takes the square root of $x$.

Then, we have $h(x) = f(g(x)) = \sqrt{9x - 5}$, where $f(g(x))$ means $f$ acting on the result of $g(x)$, which matches the given $h(x)$.

So, you can express:

• $g(x) = 9x - 5$
• $f(x) = \sqrt{x}$

Would you like to know more about how these functions interact or about other ways to decompose functions?

Related Questions:

1. What happens if you choose different inner functions for $g(x)$?
2. How does changing $g(x)$ affect $f(x)$ in composition?
3. Could $f(x)$ and $g(x)$ be swapped while maintaining the same $h(x)$?
4. What are the domains of $f(x)$ and $g(x)$ in this composition?
5. How does the graph of $h(x)$ compare to the graphs of $f(x)$ and $g(x)$?

Tip: When choosing functions for composition, always ensure that the output of the inner function $g(x)$ matches the required input type and range of the outer function $f(x)$.