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Math Help - another graph

  1. #1
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    another graph

    i have attached this problem
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  2. #2
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    Quote Originally Posted by carlasader View Post
    i have attached this problem
    Hello,

    if
    h(x) = x
    f(x) = x-1
    g(x) = 2x

    Then you get the required function:
    1. Plug in the term of f(x) into h: h(f(x)) = (x-1)^3
    2. Now plug in this term into g:

    g(h(f(x))) = 2 \cdot (x-1)^3

    To calculate the equation of the inverse function you change the x and y-values:

    y = 2(x-1)^2 ~ \Longrightarrow ~ x = 2(y-1)^2 . Now solve for y and you'll get:

    y = 1 + \sqrt[3]{\frac{1}{2} x}

    1. The graph of the inverse function is the inflection of the graph of the function at the line y = x
    2. Therefore the graph of the inverse function and the original function intersect on the line y = x (if there are any intersections, of course)
    3. The zeros of the original function are the y-intercepts of the inverse function; The y-intercepts of the original function are the zeros of the inverse function.
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