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* g)(x)=f(x)* g(x)\\\\(f* g)(x)=(3x+2)(x^2+1)=3x^3+3x+2x^2+2=\boxed{3x^3+2x^2+3x+2}`

Answer 2

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

Explanation:

Given : If
`f(x) = 3x + 2` and
`g(x)=x^2+1`

To find : Which expression is equivalent to
`(f* g) (x)`?

Solution :

We can write,

`(f* g) (x)=f(x)* g(x)` ....(1)

We know,
`f(x) = 3x + 2` and
`g(x)=x^2+1`

Substituting the values in (1),

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

Multiply term by term,

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

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

Therefore, The expression is equivalent to
`(f* g) (x)=3x^3+2x^2+3x+2`