Answer:
\((f\times g) (x)=3x^3+2x^2+3x+2\)
Step-by-step explanation:
Given : If \(f(x) = 3x + 2\) and \(g(x)=x^2+1\)
To find : Which expression is equivalent to \((f\times g) (x)\)?
Solution :
We can write,
\((f\times g) (x)=f(x)\times g(x)\) ....(1)
We know, \(f(x) = 3x + 2\) and \(g(x)=x^2+1\)
Substituting the values in (1),
\((f\times g) (x)=(3x+2)\times (x^2+1)\)
Multiply term by term,
\((f\times g) (x)=3x^3+3x+2x^2+2\)
\((f\times g) (x)=3x^3+2x^2+3x+2\)
Therefore, The expression is equivalent to \((f\times g) (x)=3x^3+2x^2+3x+2\)
