# Algebra

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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 -

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 -

This is as far as I got. Is this correct? Thanks!

g(f(x))
= g(x^2-3)
= 2(x^2-3) + 1

• Algebra -

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 -

Thanks for your help! I really appreciate it!

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That is not what the ? is asking. The ? is asking about how to get the quotient function, not the composite as you solved for. Can you please show us how to get the quotient function solution?
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