Posted by **Breanna** on Friday, June 12, 2009 at 11:44pm.

Given that f(x) = x^2-3 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^2-3)

= 2(x^2-3) + 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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