Question

\begin{aligned}
f(x)&=x^2\\\\
g(x)&=3x^2
\end{aligned}

Answer 1

It looks like you've defined two functions:

1. \( f(x) = x^2 \)
2. \( g(x) = 3x^2 \)

If you need to perform operations on these functions (like addition, subtraction, composition, etc.), or if you have specific questions about them, please let me know! Here are some common operations you could consider:

### Addition
\[
(f + g)(x) = f(x) + g(x) = x^2 + 3x^2 = 4x^2
\]

### Subtraction
\[
(f - g)(x) = f(x) - g(x) = x^2 - 3x^2 = -2x^2
\]

### Multiplication
\[
(f \cdot g)(x) = f(x) \cdot g(x) = x^2 \cdot 3x^2 = 3x^4
\]

### Division
\[
\frac{f}{g}(x) = \frac{f(x)}{g(x)} = \frac{x^2}{3x^2} = \frac{1}{3} \quad \text{for } x \neq 0
\]

### Composition
\[
(f \circ g)(x) = f(g(x)) = f(3x^2) = (3x^2)^2 = 9x^4
\]

\[
(g \circ f)(x) = g(f(x)) = g(x^2) = 3(x^2)^2 = 3x^4
\]

Feel free to ask if you have a specific operation in mind or if you'd like to explore further concepts related to these functions!