Thank you for sharing the image of these composition function problems. Let’s tackle the first one, and I will provide a step-by-step solution.

Soal 1:

Given:

• $f(x) = 2x + 3$
• $g(x) = x^2$

We need to find:

1. $(f \circ g)(x)$
2. $(g \circ f)(x)$

1. $(f \circ g)(x)$

The composition $(f \circ g)(x)$ means applying $g(x)$ first and then applying $f$. Mathematically: $(f \circ g)(x) = f(g(x))$ Substitute $g(x) = x^2$ into $f(x) = 2x + 3$: $f(g(x)) = f(x^2) = 2(x^2) + 3 = 2x^2 + 3$ So, $(f \circ g)(x) = 2x^2 + 3$.

2. $(g \circ f)(x)$

The composition $(g \circ f)(x)$ means applying $f(x)$ first and then applying $g$. Mathematically: $(g \circ f)(x) = g(f(x))$ Substitute $f(x) = 2x + 3$ into $g(x) = x^2$: $g(f(x)) = g(2x + 3) = (2x + 3)^2 = 4x^2 + 12x + 9$ So, $(g \circ f)(x) = 4x^2 + 12x + 9$.

Now, I will proceed with solving the remaining problems. Would you like me to continue with the next problem (Soal 2)? Feel free to ask for further clarifications!

Here are 5 related questions you can explore:

1. What are the properties of function compositions?
2. How do you find the domain of a composed function?
3. What happens when functions are inverses in composition?
4. Can you compose more than two functions? How is this done?
5. How can function composition be applied to real-world problems?

Tip: Always substitute the inner function first when dealing with compositions.