Question

9. Solve (x+3)(x-2);
2=1, Hence, find s, in
3 2
-=1
X+ s
$\\ \frac{(x + 2)}{3} - \frac{(x - 2}{2}$
​

Answer 1

Answer:

Step-by-step explanation:

Let's look an example to see how this works.

Given that f(x)=2x-3f(x)=2x−3f, left parenthesis, x, right parenthesis, equals, 2, x, minus, 3 and g(x)=x+1g(x)=x+1g, left parenthesis, x, right parenthesis, equals, x, plus, 1, find (f\cdot g)(x)(f⋅g)(x)left parenthesis, f, dot, g, right parenthesis, left parenthesis, x, right parenthesis.

Solution

The most difficult part of combining functions is understanding the notation. What does (f\cdot g)(x)(f⋅g)(x)left parenthesis, f, dot, g, right parenthesis, left parenthesis, x, right parenthesis mean?

Well, (f\cdot g)(x)(f⋅g)(x)left parenthesis, f, dot, g, right parenthesis, left parenthesis, x, right parenthesis just means to find the product of f(x)f(x)f, left parenthesis, x, right parenthesis and g(x)g(x)g, left parenthesis, x, right parenthesis. Mathematically, this means that (f\cdot g)(x)=f(x)\cdot g(x)(f⋅g)(x)=f(x)⋅g(x)left parenthesis, f, dot, g, right parenthesis, left parenthesis, x, right parenthesis, equals, f, left parenthesis, x, right parenthesis, dot, g, left parenthesis, x, right parenthesis.

Now, this becomes a familiar problem.

\begin{aligned} (f\cdot g)(x) &= f(x)\cdot g(x)&\gray{\text{Define.}} \\\\ &= \left(2x-3\right)\cdot\left(x+1\right) &\gray{\text{Substitute.}} \\\\ &= 2x^2+2x-3x-3&\gray{\text{Distribute.}} \\\\ &=2x^2-x-3&\gray{\text{Combine like terms.}} \end{aligned}  

(f⋅g)(x)

​    

=f(x)⋅g(x)

=(2x−3)⋅(x+1)

=2x  

2

+2x−3x−3

=2x  

2

−x−3

​    

Define.

Substitute.

Distribute.

Combine like terms.

​