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Math Help - Can someone show me how to solve these few problems step by step.

  1. #1
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    Can someone show me how to solve these few problems step by step.

    1. Given f(x)=x^2 and g(x)=(-7/x) find f(g(x)) and g(f(x))

    2. Let f(x)=x+2 and g(x)= X^2-15, find f(g(4)) and g(f(4))

    3. Let f(x)= (x-5/12), find f^-1(x)

    4. Which of the following functions are one to one?
    f(x)=|x+3|
    g(x)=x^2
    h(x)= sqrt(4-4x)
    k(x)=x^3
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  2. #2
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    Quote Originally Posted by roxy6 View Post
    1. Given f(x)=x^2 and g(x)=(-7/x) find f(g(x)) and g(f(x))

    f[g(x)] = f(-7/x) = (-7/x)^2 = 49/x^2

    g[f(x)] = g(x^2) = -7/x^2

    2. Let f(x)=x+2 and g(x)= X^2-15, find f(g(4)) and g(f(4))

    g(4) = 1 ... f(4) = 6

    f[g(4)] = f(1) = 3

    g[f(4)] = g(6) = 21


    3. Let f(x)= (x-5/12), find f^-1(x)

    y = (x-5)/12

    swap x and y ...

    x = (y-5)/12

    12x = y-5

    y = f^{-1}(x) = 12x + 5


    4. Which of the following functions are one to one?
    f(x)=|x+3|
    g(x)=x^2
    h(x)= sqrt(4-4x)
    k(x)=x^3

    first, you find out what one-to-one means ...
    ...
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