Question

If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f*g) (x)?

Answer 1

 (f*g) (x) = (3x + 2) (x^2 + 1)
 (f*g) (x) = 3x^3 + 3x + 2x^2 + 2
 (f*g) (x) = 3x^3 + 2x^2 + 3x + 2

Answer 2

Answer:  The required expression is $3x^3+2x^2+3x+2.$

Step-by-step explanation:  We are given the following two functions :

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

We are to find the expression equivalent to $(f*g)(x).$

We know that

for any two functions p(x) and q(x), we have

$(p*q)(x)=p(x)\times q(x).$

Therefore, we get

$(f*g)(x)\\\\=f(x)\times g(x)\\\\=(3x+2)(x^2+1)\\\\=x^2(3x+2)+1(3x+2)\\\\=3x^3+2x^2+3x+2.$

Thus, the required expression is $3x^3+2x^2+3x+2.$