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March 25, 2017

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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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