To solve $(g \circ f)(2)$, we first break it into steps:

Step 1: Understand the composite function

The composite function $(g \circ f)(x)$ means $g(f(x))$. This involves finding $f(x)$ first, then substituting it into $g(x)$.

Step 2: Find $f(2)$

The given $f(x) = 2x - 4$: $f(2) = 2(2) - 4 = 4 - 4 = 0$

Step 3: Find $g(f(2)) = g(0)$

The given $g(x) = 4x^2 + 3$: $g(0) = 4(0)^2 + 3 = 0 + 3 = 3$

Final Answer:

$(g \circ f)(2) = 3$

Would you like additional explanation or further questions related to this problem?

Related Questions:

1. What is the general form of $(g \circ f)(x)$ for these specific functions?
2. How do you find $(f \circ g)(x)$ and compare it to $(g \circ f)(x)$?
3. What happens if $g(x)$ is replaced with $g(x) = x^3 - 2x + 1$?
4. Can the composite function $g(f(x))$ ever equal zero? If so, for what values of $x$?
5. How does the domain of $f(x)$ and $g(x)$ influence the composite function?

Tip:

Always simplify and check the intermediate values when dealing with composite functions to avoid calculation errors.