Question

For the given functions f and g, find the requested function and state its domain.

Answer 1

So we have the following functions:

$\begin{gathered} f(x)=16-x^2 \\ g(x)=4-x \end{gathered}$

And we have to find their sum f+g. We just need to add their expressions:

$\begin{gathered} (f+g)(x)=16-x^2+4-x \\ \text{We can add the two constants 4 and 16:} \\ \mleft(f+g\mright)\mleft(x\mright)=-x^2-x+20 \end{gathered}$

And what we have is a quadratic function, The domain of this type of functions is equal to all real numbers so the correct option is the first one.