To find \((f * g)(x)\), you need to multiply the two functions \(f(x)\) and \(g(x)\).
Given:
- \(f(x) = 3x^2\)
- \(g(x) = 5 - x\)
The product \((f * g)(x)\) is computed as follows:
\[ (f * g)(x) = f(x) \cdot g(x) \]
Substituting in the expressions for \(f(x)\) and \(g(x)\):
\[ (f * g)(x) = (3x^2)(5 - x) \]
Now, distribute \(3x^2\) across \(5 - x\):
\[ (f * g)(x) = 3x^2 \cdot 5 - 3x^2 \cdot x \]
Calculating that gives:
\[ (f * g)(x) = 15x^2 - 3x^3 \]
So the final result is:
\[ (f * g)(x) = 15x^2 - 3x^3 \]