Question

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

Answer 1

$f(x)=3x+2\\The\ domain\ D_f=\mathbb{R}\\\\g(x)=x^2+1\\The\ domain\ D_G=\mathbb{R}\\\\D_f=D_g\ therefore\ (f\times g)(x)=f(x)\times g(x)\\\\(f\times g)(x)=(3x+2)(x^2+1)=3x^3+3x+2x^2+2=\boxed{3x^3+2x^2+3x+2}$

Answer 2

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  $(f\times g) (x)=3x^3+2x^2+3x+2$