Posted by Breanna on .
Given that f(x) = x^23 and g(x) = 2x+1, find each of the following, if it exists.
a. (fg)(root3)
b. (gf)(1/2)

Algebra 
drwls,
a. Determine what g(sqrt3) is and call it x. Then calculate f(x)
x = g(sqrt3) = 2 sqrt3 +1
f(x) = x^2 3 = 12 4 sqrt3 +1  3
= 10  4 sqrt3
Do b the same way. 
Algebra 
Breanna,
This is as far as I got. Is this correct? Thanks!
g(f(x))
= g(x^23)
= 2(x^23) + 1 
Algebra 
drwls,
What you wrote for g(f(x))is correct. As a final step, they want you to substitute 1/2 for x.
I skipped the step of writing down the
g(f) function. You can start inserting 1/2 for x directly
f(1/2) = (1/2)^2 3 = 2 3/4
= 11/4
g(f(1/2)) = 22/4 +1 = 18/4 = 4 1/2 
Algebra 
Jasmin,
Thanks for your help! I really appreciate it!