Answer:
[tex](FxG)(x)=3x^2+11x+10[/tex].
Step-by-step explanation:
This is a simple multiplication of functions. In order to get a result, we must find the product generated by the multiplication of the arguments of both functions.
1. Write the arguments.
[tex]F(x)= x+2\\ \\G(x)=3x+5[/tex]
2. Multiply the arguments.
[tex](x+2)(3x+5)[/tex]
Using the associative property of multiplication, rewrite the expression.
This is the rule we are applying: [tex](a+b)(c+d)=(a)(c)+(a)(d)+(b)(c)+(b)(d)[/tex]
Rewriting:
[tex](x)(3x)+(x)(5)+(2)(3x)+(2)(5)\\ \\(3x^2)+(5x)+(6x)+(10)\\\\3x^2+11x+10[/tex]
3. Express your result.
[tex](FxG)(x)=3x^2+11x+10[/tex].
