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Math Help - composite functions

  1. #1
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    composite functions

    Hello people,

    i need a bit of help with these proofs, its one of those things were i can't sport what to do with the thing next.

    1) f(x)=2x +lnx, g(x) = e^2x, prove that gf(x)=4e^4x

    2) (cosec x)^4 - (cot x)^4 = (cosec x )^2 + (cot x)^2

    3)

    P= (2800ae^0.2t)/(1 +ae^0.2t) a=0.12

    show that p = 336/(0.12 + e^-0.2t)
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  2. #2
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    Quote Originally Posted by sillyhacker View Post
    i need a bit of help with these proofs, its one of those things were i can't sport what to do with the thing next.

    1) f(x)=2x +lnx, g(x) = e^2x, prove that gf(x)=4e^4x
    gf(x) = g(f(x) = e^2(f(x)) = e^{4x + 2 ln(x)) = e^{4x} e^{2ln(x)}

    .............. = e^{4x} [e^{ln(x)}]^2 = e^{4x} x^2

    (since e^ln(x) = x).

    RonL
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sillyhacker View Post
    2) (cosec x)^4 - (cot x)^4 = (cosec x )^2 + (cot x)^2
    Here's (2)
    Attached Thumbnails Attached Thumbnails composite functions-proof.gif  
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sillyhacker View Post
    3)

    P= (2800ae^0.2t)/(1 +ae^0.2t) a=0.12

    show that p = 336/(0.12 + e^-0.2t)
    P = (2800ae^0.2t)/(1 +ae^0.2t) .............................. plug in a = 0.12
    => P = [2800(0.12)e^(0.2t)]/[1 + 0.12e^(0.2t)] ..........now simplify
    => P = [336e^(0.2t)]/[1 + 0.12e^(0.2t)]
    => P = 336/{e^(-0.2t)[1 + 0.12e^(0.2t)]}
    => P = 336/[0.12e^(0.2t) * e^(-0.2t) + e^(-0.2t)]
    => P = 336/(0.12 + e^-0.2t)
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  5. #5
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    thank you for your help.
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