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college algebra

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Let
f(x) = 1/x − 2
and
g(x) = 1/x − 3

. Determine the domain of the composite function. (Enter your answer using interval notation.)

g compose f
_____?

& Find the composite function.

(g compose f)(x) = _____?

  • college algebra -

    g(f) = 1/(f-3) = 1/(1/(x-2)-3) = (2-x)/(3x-7)

    So, the domain is all reals except where
    3x-7 = 0
    or
    x-2=0 (because f(2) is not defined)
    or
    f(x) = 3 (because g(3) is not defined)

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