Posted by Lola on .
Hi there, I need help with composition of functions.
I need to find fog, gof, gog, and fof and their domains for the following:
f(x) = square root of 2x +3
g(x) = x^2 + 1
if someone can help me asap that would be so great!

Calculus 
drwls,
For g of f, substitute sqrt(2x +3) for x in g(x)
You get (2x + 3) + 1 = 2x + 4
The domain is all numbers in thnis case.
Do the others the same way. We will gladly critique your work. 
Calculus 
Lola,
okay, so i tried out subtsting x into f (x) and i got sqrt (2x^2 +5)..is that right?
and what do u mean domain is all in numbers?
can u help me with the f o f and g og?
and a side question, we got a table of values that was something like
x 1 2 3 4 5 6
f(x) 3 1 .....
g(x) 6
so the first question is like evaulaute:
f(g(1))
would that be
3(6)? 
Calculus 
drwls,
Are you trying to calculate f of g(x)?
Assuming f(x) = sqrt(2x+3) and not sqrt (2x) + 3, f of g(x) would be
sqrt [2(x^2 +1) + 3]= sqrt (2x^2 + 5)
So you would be correct.
g of g(x) = (x^2+1)^2 +1 = x^2 + 2x + 2
To your side question: yes, the first answer is 18.