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Math Help - Algebra Proofs

  1. #1
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    Algebra Proofs

    (1) If f(x) = a^x, show that f(A + B) = f(A) * f(B)

    (2) If f(x) = a^x, show that f(Ax) = [f(x)]^A
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  2. #2
    Senior Member nikhil's Avatar
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    Quote Originally Posted by magentarita View Post
    (1) If f(x) = a^x, show that f(A + B) = f(A) * f(B)

    (2) If f(x) = a^x, show that f(Ax) = [f(x)]^A
    f(x) = a^x
    f(A + B)=a^(A + B)
    =a^A*a^B
    but a^A =f(A) and a^B=f(B)
    putting these values we get
    f(A + B) = f(A) * f(B) hence proved
    2)f(x) = a^x
    f(Ax) =a^(Ax)
    =(a^x)^A
    =[f(x)]^A
    therfor
    f(Ax) =[f(x)]^A hence proved
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  3. #3
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    (1) f(x)~=~a^x
     \implies~f(A)~=~a^A~,
     ~f(B)~=~a^B~,
     ~f(A+B)~=~a^{A+B}~=~a^A \cdot a^B~=~f(A) \cdot f(B)

    (2) f(x)~=~a^x
     \implies~f(Ax)~=~a^{Ax}~=~(a^x)^A~=~[f(x)]^A
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  4. #4
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    Excellent work!

    Wonderfully done!
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