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Math Help - Solving for an inverse function

  1. #1
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    Unhappy Solving for an inverse function

    Help me solve these questions please and thank you.

    1. Given f(x) = x2 + 3x -3 and g(x) = f -1(x) , find the value(s) of g(1).

    2. given the function f(x) = 5/ 5x-16
    a) Determine the inverse function
    b) Explain how to find the domain and range of the function and its inverse.

    3. a) Explain how you can use algebraic reasoning, rather than a vertical line test , to decide if a relation is a function?

    b) How can you determine if the inverse of a function is a function by looking at the original graph of the function?
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  2. #2
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    Re: Solving for an inverse function

    Quote Originally Posted by sabiha1995 View Post
    Help me solve these questions please and thank you.

    1. Given f(x) = x2 + 3x -3 and g(x) = f -1(x) , find the value(s) of g(1).

    2. given the function f(x) = 5/ 5x-16
    a) Determine the inverse function
    b) Explain how to find the domain and range of the function and its inverse.

    3. a) Explain how you can use algebraic reasoning, rather than a vertical line test , to decide if a relation is a function?

    b) How can you determine if the inverse of a function is a function by looking at the original graph of the function?
    1. hint .. f(x) = 1 \implies g(1) = x

    2. a) x = \frac{5}{5y-16} ... solve for y = f^{-1}(x)

    b) since an inverse swaps the x and y values of a function, what would that do to the domain and range?

    3. a) f(x) be a unique value for every value of x in the domain

    b) heard of the horizontal line test?
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    Re: Solving for an inverse function

    Quote Originally Posted by skeeter View Post
    1. hint .. f(x) = 1 \implies g(1) = x

    2. a) x = \frac{5}{5y-16} ... solve for y = f^{-1}(x)

    b) since an inverse swaps the x and y values of a function, what would that do to the domain and range?

    3. a) f(x) be a unique value for every value of x in the domain

    b) heard of the horizontal line test?
    I wonder how is g defined in this case
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  4. #4
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    Re: Solving for an inverse function

    Quote Originally Posted by psolaki View Post
    I wonder how is g defined in this case
    apparently, not as a function ...

    ... find the value(s) of g(1).
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    Re: Solving for an inverse function

    Quote Originally Posted by skeeter View Post
    apparently, not as a function ...
    if as a relation then how dowe define the composition of gof??
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    Re: Solving for an inverse function

    Quote Originally Posted by psolaki View Post
    if as a relation then how dowe define the composition of gof??
    If f is a function and g is its inverse function, then f \circ g = g \circ f = x

    I don't believe function composition can be applied to relations in general. I'm not an algebraist, so I would need to rely on someone with more knowledge to answer this query.
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