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Math Help - Functions

  1. #1
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    Functions

    If f(x) = 4x + 3 and h(x) = 8x^2 -1.
    a) Find x so that f(x) = h(x)
    b) Find a function g(x) so that f(g(x)) = h(x)

    can someone exaplin to me how to do this?
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  2. #2
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    Quote Originally Posted by foreverbrokenpromises View Post
    If f(x) = 4x + 3 and h(x) = 8x^2 -1.
    a) Find x so that f(x) = h(x)
    b) Find a function g(x) so that f(g(x)) = h(x)

    can someone exaplin to me how to do this?

    Part a) Let f(x) = h(x) = y. Now solve y = 4x + 3 and y = 8x^2 - 1 simultaneously.

    Part b) Since f(g(x)) means substitute every x value in f(x) with function g(x), basically it wants you to solve this:

     4[g(x)] + 3 = 8x^2 - 1
    You need to find a function g(x) in terms of x to make the LHS = RHS.
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  3. #3
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    a) solve 4x + 3 = 8x^2 -1. you should be able to do this

    b) if f(g(x)) = h(x) then f^{-1}(f(g(x))) = f^{-1}(h(x)) or g(x) = f^{-1}(h(x))
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  4. #4
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    Quote Originally Posted by Gusbob View Post
    Part a) Let f(x) = h(x) = y. Now solve y = 4x + 3 and y = 8x^2 - 1 simultaneously.

    Part b) Since f(g(x)) means substitute every x value in f(x) with function g(x), basically it wants you to solve this:

     4[g(x)] + 3 = 8x^2 - 1
    You need to find a function g(x) in terms of x to make the LHS = RHS.

    for a) i got x = -1/2 or x =1
    is that just the answer
    or is it just one of them?
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  5. #5
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    They are both correct. There are two points where the curves intersect.
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