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Thread: Solve determining inverse functions

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    Solve determining inverse functions

    Determine wether f(x) = 3x + 8 and g(x) = x - 8 / 3 are inverse functions.


    For f(x) = 3x - 19, find the inverse f-(x). Minus sign is supposed to be uppercase..
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    Re: Solve determining inverse functions

    If $f(x)$ and $g(x)$ are inverse functions, then $f[g(x)]=g[f(x)] = x$



    For the second problem, swap variables ...

    $x=3y-19$

    ... solve for $y$
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    Re: Solve determining inverse functions

    Is g(x)= x- 8/3 or is it (x- 8)/3? That is an important difference!
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    Re: Solve determining inverse functions

    Quote Originally Posted by HallsofIvy View Post
    Is g(x)= x- 8/3 or is it (x- 8)/3? That is an important difference!
    While true you have managed so far to not sink to Plato's level of questioning the obvious.

    Please Dr., don't go there.
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    Re: Solve determining inverse functions

    Quote Originally Posted by romsek View Post
    While true you have managed so far to not sink to Plato's level of questioning the obvious.
    That's often a good thing...

    -Dan
    Thanks from Plato
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    Re: Solve determining inverse functions

    Quote Originally Posted by topsquark View Post
    That's often a good thing...
    -Dan
    That is particularly true when one is qualified to comment.
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    Re: Solve determining inverse functions

    Quote Originally Posted by HallsofIvy View Post
    Is g(x)= x- 8/3 or is it (x- 8)/3? That is an important difference!
    x - 8
    3
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    Re: Solve determining inverse functions

    I may have to "sink to Plato's level" (that would be a bad thing???). I don't think it was at all "obvious" that when the OP wrote "x- 8/3" he meant "(x- 8)/3".
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    Re: Solve determining inverse functions

    Thanks, skeeter! Sorry, I'm kind of new to this.. but I'm kind of stuck with proving g[f(x)]=x. The first one should be the following, right?

    1. Determine wether f(x) = 3x + 8 and g(x) = x - 8 / 3 are inverse functions.

    f[g(x)] = f[(x - 8) / 3]
    = 3x [(x - 8) / 3] + 8
    = x - 8 + 8
    = 8

    g[f(x)] = g(3x + 8)
    ..and then how would you continue? Or would you've done it differently?

    2. I understood this one.. should be the following?

    f^-1(x) = (x + 19) / 3

    Br,
    Evan
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    Re: Solve determining inverse functions

    Quote Originally Posted by Griegevan View Post
    Thanks, skeeter! Sorry, I'm kind of new to this.. but I'm kind of stuck with proving g[f(x)]=x. The first one should be the following, right?

    1. Determine wether f(x) = 3x + 8 and g(x) = x - 8 / 3 are inverse functions.

    f[g(x)] = f[(x - 8) / 3]
    = 3x [(x - 8) / 3] + 8
    = x - 8 + 8
    = 8

    g[f(x)] = g(3x + 8)
    ..and then how would you continue? Or would you've done it differently?

    2. I understood this one.. should be the following?

    f^-1(x) = (x + 19) / 3

    Br,
    Evan
    f[g(x)] = 3g(x)+8 = \cancel{3}\left(\dfrac{x-8}{\cancel{3}}\right)+8 = (x-8)+8 = x

    g[f(x)] = \dfrac{f(x)-8}{3} = \dfrac{(3x+8)-8}{3} = \dfrac{3x}{3} = x

    So, f^{-1}(x) = g(x).

    For the second one, yes, f(x) = 3x-19 \Longrightarrow f^{-1}(x) = \dfrac{x+19}{3}
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  11. #11
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    Re: Solve determining inverse functions

    Quote Originally Posted by Griegevan View Post
    Thanks, skeeter! Sorry, I'm kind of new to this.. but I'm kind of stuck with proving g[f(x)]=x. The first one should be the following, right?

    1. Determine wether f(x) = 3x + 8 and g(x) = x - 8 / 3 are inverse functions.

    f[g(x)] = f[(x - 8) / 3]
    = 3x [(x - 8) / 3] + 8
    = x - 8 + 8
    = 8

    check this again ...

    g[f(x)] = g(3x + 8)
    ..and then how would you continue? Or would you've done it differently?

    g(3x+8) = [(3x+8) - 8]/3 = ... continue

    2. I understood this one.. should be the following?

    f^-1(x) = (x + 19) / 3

    Br,
    Evan
    ...
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