Question

Let f(x) = 2x2 + x − 3 and g(x) = x + 2.

Find (f • g)(x)

Answer 1

2x^3+5x^2-x-6

Explanation:

f(x) = 2x^2 + x − 3 and g(x) = x + 2.

(f • g)(x) = (2x^2 + x − 3 ) * (x + 2)

Distribute

= (2x^2 + x − 3 )*x + (2x^2 + x − 3 )*2

= 2x^3 +x^2 -3x + 4x^2 +2x -6

Combine like terms

=2x^3+5x^2-x-6

Answer 2

`(f\cdot g)(x) = 2x^3 + 5x^2-x-6`

Explanation:

We are given the two functions:

`f(x)=2x^2+x-3\text{ and } g(x)=x+2`

And we want to find:

`(f \cdot g)(x)`

Recall that this is equivalent to:

`=f(x)\cdot g(x)`

Substitute. Hence:

`(f\cdot g)(x)= (2x^2+x-3)(x+2)`

Expand if desired:

`\displaystyle = x(2x^2+x-3)+2(2x^2+x-3) \\ \\ = (2x^3+x^2-3x)+(4x^2+2x-6) \\ \\\ = 2x^3 + 5x^2-x-6`