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Math Help - Inverse functions, solving equations.

  1. #1
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    Inverse functions, solving equations.

    1) If f (x) = 3 - 2x , calculate the value of f -1 (5) .

    2) If x ^2 + y ^2 = 25 and x ^2 - y ^2 = 7 then x ^4 - y ^4 equals?
    Last edited by mr fantastic; October 28th 2009 at 03:50 AM. Reason: Changed post title.
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  2. #2
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    Quote Originally Posted by sri340 View Post
    1) If f (x) = 3 - 2x , calculate the value of f -1 (5) .
    2) If x ^2 + y ^2 = 25 and x ^2 - y ^2 = 7 then x ^4 - y ^4 equals?
    1)
    f (x) = 3 - 2x = y(say)
    y=3-2x \quad \Rightarrow x=\frac{(3-y)}{2}
     \ f^{-1} (y) = \frac{(3-y)}{2} \quad (\because f(x)=y)
    \therefore \boxed { f^{-1} (x) = \frac{(3-x)}{2}}
    to find f^{-1}( 5)  put x= 5 in above equation

    2) If x ^2 + y ^2 = 25 and x ^2 - y ^2 = 7 then x ^4 - y ^4 equals?
    2) use  x^4-y^4=(x^2+y^2) \cdot (x^2-y^2)
    (because a^2-b^2=(a+b)(a-b)
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