The problem in the image states:

3. a. Jika $h(x) = (x-3)^3$ dan $h(x) = f \circ g$, tentukan fungsi $f$ dan $g$.

Translation: 3. a. If $h(x) = (x-3)^3$ and $h(x) = f \circ g$, determine the functions $f$ and $g$.

Solution:

The expression $h(x) = f(g(x))$ implies that the function $g$ is applied first, followed by the function $f$.

Let’s set:

• $g(x) = x-3$, so the inner function shifts the input by 3.
• Then, $f(u) = u^3$, where $u = g(x)$.

Thus, $f(g(x)) = (x-3)^3$, which matches $h(x)$.

Therefore, the functions are:

• $g(x) = x-3$
• $f(u) = u^3$

Would you like more details, or do you have any questions?

Related Questions:

1. How can we verify if $f(g(x))$ correctly gives $h(x)$?
2. What are the steps for finding $f$ and $g$ if $h(x)$ were more complicated?
3. Can we choose different functions $f$ and $g$ that still satisfy $h(x) = f \circ g$?
4. How does composition of functions differ from addition or multiplication of functions?
5. What is the significance of function composition in solving real-world problems?

Tip:

When decomposing a function $h(x)$ into $f(g(x))$, start by identifying a simple transformation that can be applied first (like a shift or scaling) and then determine the remaining function.