In the image, the problem asks for the composition $(f \circ f)(x)$, which means applying the function $f(x)$ to itself. Let's break it down.

Given:

• $f(x) = 2x$
• $h(x) = 3 - 4x$ (though this isn't directly needed for the current problem).

We need to find: $(f \circ f)(x) = f(f(x))$

Step-by-step solution:

1. Start with $f(x) = 2x$.
2. Now substitute $f(x)$ into itself: $f(f(x)) = f(2x)$
3. Since $f(x) = 2x$, apply this to $2x$: $f(2x) = 2(2x) = 4x$

Thus, $(f \circ f)(x) = 4x$.

Let me know if you'd like more details or if you have any questions! Here are some related questions:

1. What is $(h \circ h)(x)$ if $h(x) = 3 - 4x$?
2. How would you compute $(f \circ h)(x)$?
3. What is the composition of $(h \circ f)(x)$?
4. How does the order of function composition affect the result?
5. Can you generalize $(f \circ f)(x)$ for different linear functions?

Tip: When working with function compositions, always start by evaluating the inner function first, then substitute the result into the outer function.