Question

Suppose that the functions of f and g are as follows
f(x) = 2x+3
g(x)= (sqrt 4x-5)
Find f*g and f+g. Then give their domain using interval notation

(f*g)(x)=
Domain of f*g:

(f+g)(x)=
Domain of f+g:

Answer 1

\[f+g(x)=f(x)+g(x)\] add them up

Answer 2

for domain of \(\sqrt{4x-5}\) you have to make sure that \(4x-5\) is not negative, because you cannot take the square root of a negative number
set \(4x-5\geq 0\) and solve for \(x\)