Question

f(x)=3x-2
g(x)=x+3
find (f × g)(x)
a)3x^2+7x-6
b)3x^2-6
c)3x^3+7x^2-6x
d)3x^2+11x-6

Answer 1

To find \((f \times g)(x)\), we need to multiply the functions \(f(x)\) and \(g(x)\):

1. Given:
\[
f(x) = 3x - 2
\]
\[
g(x) = x + 3
\]

2. Now, calculate \((f \times g)(x) = f(x) \cdot g(x)\):
\[
(f \times g)(x) = (3x - 2)(x + 3)
\]

3. Expand the expression using the distributive property (FOIL):
\[
= 3x \cdot x + 3x \cdot 3 - 2 \cdot x - 2 \cdot 3
\]
\[
= 3x^2 + 9x - 2x - 6
\]

4. Combine like terms:
\[
= 3x^2 + (9x - 2x) - 6
\]
\[
= 3x^2 + 7x - 6
\]

Thus, \((f \times g)(x) = 3x^2 + 7x - 6\).

So, the answer is:
**a) \(3x^2 + 7x - 6\)**.