Posted by Breanna on Friday, June 12, 2009 at 11:44pm.
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, Saturday, June 13, 2009 at 12:43am
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, Saturday, June 13, 2009 at 12:47am
This is as far as I got. Is this correct? Thanks!
g(f(x))
= g(x^23)
= 2(x^23) + 1

Algebra  drwls, Saturday, June 13, 2009 at 6:23am
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, Saturday, June 13, 2009 at 9:00am
Thanks for your help! I really appreciate it!
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