Question

find (f*g) (x)
for f(x)=3x2^ and g(x)=5-x

Answer 1

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:

\[
(f * g)(x) = 15x^2 - 3x^3
\]