posted by Breanna .
Given that f(x) = x^2-3 and g(x) = 2x+1, find each of the following, if it exists.
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.
This is as far as I got. Is this correct? Thanks!
= 2(x^2-3) + 1
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
g(f(1/2)) = -22/4 +1 = -18/4 = -4 1/2
Thanks for your help! I really appreciate it!