Question

Given f(x) = 2x-5 and g(x) = 6x + 3, which is the rule for (x) g(x)?

Answer 1

Given

$\begin{gathered} f(x)=2x-5 \\ g(x)=6x+3 \end{gathered}$

We would like to know the multiplicacion. To multiply functions we have to remember the rule

$(fg)(x)=f(x)g(x)$

Then, in this case we have

$\begin{gathered} (fg)(x)=f(x)g(x) \\ =(2x-5)(6x+3) \\ =12x^2+6x-30x-15 \\ =12x^2-24x-15 \end{gathered}$

Then

$(fg)(x)=12x^2-24x-15$