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Math Help - f and g inverese of each other?

  1. #1
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    f and g inverese of each other?

    am i doing this right or am i starting it the right way?

    1st pic is the problem
    2d and 3rd are what ive done
    Attached Thumbnails Attached Thumbnails f and g inverese of each other?-problem.jpg   f and g inverese of each other?-f-g-x-.jpg   f and g inverese of each other?-g-f-x-.jpg  
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  2. #2
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    f\left(\frac{6}{x-1}\right) =

    \frac{6 + \frac{6}{x-1}}{\frac{6}{x-1}} =

    multiply numerator and denominator by (x-1) to clear the fractions ...

    \frac{6(x-1) + 6}{6} =

    \frac{6x - 6 + 6}{6} = x

    now ... you do g[f(x)] , see if you get x .
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  3. #3
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    how do I clear the fractions at the bottom

    6/[(6+x)/(x)] -1


    so if I get x for g it makes then inverse?
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  4. #4
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    Quote Originally Posted by rj2001 View Post
    how do I clear the fractions at the bottom

    6/[(6+x)/(x)] -1
    \frac{6}{\frac{6+x}{x} - 1} \cdot \frac{x}{x}


    so if I get x for g it makes then inverse?
    thought you already knew that ... if f[g(x)] = g[f(x)] = x, then f(x) and g(x) are inverses.
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  5. #5
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    Could you just find the inverse of g(x) and show that it is f(x). It would be much quicker.
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  6. #6
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    Quote Originally Posted by whipflip15 View Post
    Could you just find the inverse of g(x) and show that it is f(x). It would be much quicker.
    Yes.

    This is just another method to verify that two functions are inverses.
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