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Math Help - Functions questions

  1. #1
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    Functions questions

    Hello! I seriously need help in functions! Thank you in advance!

    Functions f and g are defined by f(x) = |x+1| , x is real, and g(x) = ln (x^2), x is real, x is not zero. Explain why fg exists and gf does not exist.

    Thank you!
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  2. #2
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    Quote Originally Posted by Tangera View Post
    Hello! I seriously need help in functions! Thank you in advance!

    Functions f and g are defined by f(x) = |x+1| , x is real, and g(x) = ln (x^2), x is real, x is not zero. Explain why fg exists and gf does not exist.

    Thank you!
    Do you mean explain why f(g(x)) exists but g(f(x)) does not?

    f(g(x)) exists if the range of g is a subset of the domain of f. The range of g is all real numbers. This is a subset of the domain of f. Therefore f(g(x)) exists.

    Note: Any set is considered a subset of itself.

    g(f(x)) exists if the range of f is a subset of the domain of g. The range of f is all real numbers greater than OR EQUAL TO zero. This is NOT a subset of the domain of g because the domain of g does NOT include zero. Therefore g(f(x)) does not exist.
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  3. #3
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    Thank you for replying so quickly! I realised I could solve this question if I had read my notes carefully. Thank you for helping!
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