Question

I need help to find the indicated operation:f(a)= a-4g(a)= a^3+3Find (f×g)(0)

Answer 1

You have this function:

$f\mleft(a\mright)=a-4$

And the other function is:

$g\mleft(a\mright)=a^3+3$

So, to find

$\mleft(f\cdot g\mright)(a)$

You need to multiply both functions, as you can see below:

$\begin{gathered} (f\cdot g)(a)=(a-4)(a^3+3) \\ (f\cdot g)(a)=(a)(a^3)+(a)(3)+(-4)(a^3)+(-4)(3) \\ (f\cdot g)(a)=a^4+3a-4a^3-12 \\ (f\cdot g)(a)=a^4-4a^3+3a-12 \end{gathered}$

Now, to find

$(f\cdot g)(0)$

You need to substitute this value and evaluate:

$a=0$

Then, you get:

$\begin{gathered} (f\cdot g)(0)=(0)^4-4(0)^3+3(0)-12 \\ (f\cdot g)(0)=-12 \end{gathered}$

The answer is:

$(f\cdot g)(0)=-12$