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Math Help - Function Question

  1. #1
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    Function Question

    Hi,

    f(x) = 3x+4

    So I found the inverse:

    f(x) = 3x+4
    x=3y+4
    x-4=3y
    y=x-4/3

    Then it asks to find the domain and range. So...could someone help me? I'm not sure on how to find them.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by lax600 View Post
    Hi,

    f(x) = 3x+4

    So I found the inverse:

    f(x) = 3x+4
    x=3y+4
    x-4=3y
    y=\frac{x-4}{3}

    Then it asks to find the domain and range. So...could someone help me? I'm not sure on how to find them.
    For your domain, do you see any restrictions for x? Can x be any real number?

    For your range, do you see any restrictions for y given any real number x? Can y be any real number:

    Both functions graph lines.
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  3. #3
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    The inverse is simply:

    f(x)^-1=(Y-4)/3

    Try drawing a simple graph of the equation to see where the domain lies.

    Note that when Y=4, x=0
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  4. #4
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    Quote Originally Posted by moolimanj View Post
    The inverse is simply:

    f(x)^-1=(Y-4)/3 Mr F says: Wrong. The inverse is a function of x, not y.

    Try drawing a simple graph of the equation to see where the domain lies.

    Mr F says: From your note below, I assume you're suggesting that the graph of y = f(x) = 3x+4 be drawn. That being the case, it's worth noting that this graph will make it clear what dom f and ran f are. This is useful since {\color{red}\text{dom} f^{-1} = \text{ran} f} and {\color{red}\text{ran} f^{-1} = \text{dom} f}.

    Note that when Y=4, x=0
    ..
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  5. #5
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    Good observation Mr F

    Apologies, I meant to put the equation as a function of x after I rearranged.

    Spot on with the point about the graph
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  6. #6
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    Quote Originally Posted by masters View Post
    For your domain, do you see any restrictions for x? Can x be any real number?

    For your range, do you see any restrictions for y given any real number x? Can y be any real number:

    Both functions graph lines.

    so I could set x as 7?
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  7. #7
    A riddle wrapped in an enigma
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    Quote Originally Posted by lax600 View Post
    so I could set x as 7?
    It would appear that you may choose any real number for x which would make the domain all real numbers.

    And in doing so, the range (values for y) would also be any real number making the range all real numbers as well.

    D=\{x|x \in \Re \}

    R=\{y|y \in \Re \}
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