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Math Help - function- f(x) and g(x)

  1. #1
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    Post function- f(x) and g(x)

    Let f(x)= 3√x+2 and g(x)= x^3-2
    Which of the following are true?

    a. g(x)=f^-1(x) for all real values of x
    b. (f o g)(x)=1 for all real values of x
    c. The function f is one-to-one.

    I think the answer is only c is true. Am I correct?

    Thanks!
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  2. #2
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    Is that 3\sqrt{x}+2 or 3\sqrt{x+2}?
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  3. #3
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    the second one you wrote...but the 3 is tiny, like inside ?? the outside of the symbol,,if you know what I mean?
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  4. #4
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    Quote Originally Posted by live_laugh_luv27 View Post
    the second one you wrote...but the 3 is tiny, like inside ?? the outside of the symbol,,if you know what I mean?
    y = \sqrt[3]{x+2}
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  5. #5
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    yes! thanks
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  6. #6
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    Quote Originally Posted by live_laugh_luv27 View Post
    yes! thanks
    Can you choose more than one answer - well hell you must to be honest. But does it say to choose more than one answer?
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  7. #7
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    Yes you can choose more than one..any combination
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  8. #8
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    For choice (b),
    (f \circ g)(x) = \sqrt[3]{(x^3 - 2) + 2}
    is this going to equal 1?


    01

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  9. #9
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    Quote Originally Posted by yeongil View Post
    For choice (b),
    (f \circ g)(x) = \sqrt[3]{(x^3 - 2) + 2}
    is this going to equal 1?


    01
    Yes...but does that mean it will equal 1 for all real numbers? Like, if you plugged a 2 in instead?
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  10. #10
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    Quote Originally Posted by live_laugh_luv27 View Post
    Yes...but does that mean it will equal 1 for all real numbers? Like, if you plugged a 2 in instead?
    try x = 2 ... does it give you a value equal to 1?
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  11. #11
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    Quote Originally Posted by skeeter View Post
    try x = 2 ... does it give you a value equal to 1?
    No, I didn't..did I do something wrong?
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  12. #12
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    Quote Originally Posted by live_laugh_luv27 View Post
    No, I didn't..did I do something wrong?
    what's that tell you about statement (b), then?
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  13. #13
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    Quote Originally Posted by skeeter View Post
    what's that tell you about statement (b), then?
    it is not correct.
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  14. #14
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    Quote Originally Posted by live_laugh_luv27 View Post
    it is not correct.
    Bingo!
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  15. #15
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    Quote Originally Posted by skeeter View Post
    Bingo!
    ok, but I am still unsure about choice a.
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