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Math Help - Inverse Functions

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    Inverse Functions

    For a lot of explanations for why something is an inverse function, my textbook will say

    "For each value of x only one value of y can be calculated, therefore, the inverse is a function"

    But how can you tell that

    y=(x+4)/3

    only has one value of y for every value of x without testing it out a million times?
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    Quote Originally Posted by juliak View Post
    For a lot of explanations for why something is an inverse function, my textbook will say

    "For each value of x only one value of y can be calculated, therefore, the inverse is a function"

    But how can you tell that

    y=(x+4)/3

    only has one value of y for every value of x without testing it out a million times?
    graph the original function and see if it passes the horizontal line test ... if any horizontal line intersects the graph of f(x) only once, then its inverse f^{-1}(x) is also a function.
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    Is there any where to tell without graphing the equation?
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    Quote Originally Posted by juliak View Post
    Is there any where to tell without graphing the equation?
    you can find the inverse itself and and determine if it is a function.
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