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Math Help - Find F-1(X), then state whether F-1(X) is a function

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    Wink Find F-1(X), then state whether F-1(X) is a function

    I need help solving this problem, can anyone do a step by step guide on how to do this?

    Find F-1(X), then state whether F-1(X) is a function.
    (The small -1 and 2 represent the powers)

    1) F(X) = X2 + 3
    (Can you also explain why it is a function?)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Brazuca View Post
    I need help solving this problem, can anyone do a step by step guide on how to do this?

    Find F-1(X), then state whether F-1(X) is a function.
    (The small -1 and 2 represent the powers)

    1) F(X) = X2 + 3
    (Can you also explain why it is a function?)
    Let y = f(x), so you would have y = x^2 + 3

    to find f^{-1}(x), switch x and y in the above equation and solve for y, that will give you f^{-1}(x)

    Remember the definition of a function: it is a relation in which EVERY element in the domain maps to one AND ONLY ONE element in the range
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    Quote Originally Posted by Jhevon View Post
    Let y = f(x), so you would have y = x^2 + 3

    to find f^{-1}(x), switch x and y in the above equation and solve for y, that will give you f^{-1}(x)

    Remember the definition of a function: it is a relation in which EVERY element in the domain maps to one AND ONLY ONE element in the range
    In the end I got "Y = (square root of X - 3)"

    Now how do I know it is a function?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Brazuca View Post
    In the end I got "Y = (square root of X - 3)"

    Now how do I know it is a function?
    what are the x's in the domain? is each x associated with only one y? if yes, then it is a function. you can do the vertical line test here on the graph as an illustration
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    Quote Originally Posted by Jhevon View Post
    what are the x's in the domain? is each x associated with only one y? if yes, then it is a function. you can do the vertical line test here on the graph as an illustration
    So would that mean a yes or a no for this? "Y = (square root of X - 3)"

    On another problem I got "Y = (cube root of X + 4) - 2" and the answer was yes, but I still don't understand why.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Brazuca View Post
    So would that mean a yes or a no for this? "Y = (square root of X - 3)"

    On another problem I got "Y = (cube root of X + 4) - 2" and the answer was yes, but I still don't understand why.
    as i said, you can do the vertical line test on the graphs. if any vertical line cuts the graph only once, it is a function.

    also, try to see if each x gives only one y. it is almost clear that these functions do.

    for instance, how do we know that x^2 + y^2 = 1 is not a function. because for x = 0, the value of the function can be +1 or -1. so we have one x giving two values.
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