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March 27, 2017

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Consider the following functions.
f(x) = x2 − 3x, g(x) =√(x+2)
(a) Find (f *g)(x). (Simplify your answer completely.)
(B)Find the domain of f *g. (Enter your answer using interval notation.)
(c) Find (g *f)(x). (Simplify your answer completely.)
(D) Find the domain of g*f. (Enter your answer using interval notation.)

  • Algebra 2 help - ,

    f*g = g*f = (x^2-3x)√(x+2)
    domain is all reals x >= -2

    If you meant ◦ instead of *, then

    (f◦g) = f(g) = g^2-3g = (x+2) - 3√(x+2)
    (g◦f) = g(f) = √(f+2) = √(x^2-3x)

    domain of f◦g is x >= -2
    domain of g◦f is x<= 0 or x>= 3

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