Question

Given f(x)=3x^2+5 and g(x)=x−2 . What is (fg)(x) ? 3x^2−x+7 3x^3−6x2+5x−10 −3x^2+x−7 3x^3−10

Answer 1

(fg)(x) = 3x³-6x²+5x-10

Explanation:

We have given two functions.

f(x)=3x²+5 and g(x)=x−2

We have to find (fg)(x).

The formula to find fg is :

(fg)(x) = f(x) × g(x)

Putting values in above formula, we have

(fg)(x) = (3x²+5)(x-2)

(fg)(x) = 3x²(x-2)+5(x-2)

(fg)(x) = 3x³-6x²+5x-10 which is the answer.

Answer 2

For this case we have that by definition:

`(fg) (x) = f (x) * g (x)`

So:

`(fg) (x) = (3x ^ 2 + 5) (x-2)`

We apply distributive property that states that:

`(a + b) (c + d) = ac + ad + bc + bd`

In addition, we take into account that:

`+ * - = -`

`(fg) (x) = 3x ^ 3-6x ^ 2 + 5x-10`

Answer:

`3x ^ 3-6x ^ 2 + 5x-10`

Option B