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    Inverse Function

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    a. Write an equation for the inverse function in the form of y=f^-1(x), b. graph f and f^-1 on the axes, and c. give the domain and the range of f and f^-1. If the function is not one-to-one, say so.

    1. y=4x-5

    2. y=4/x

    © BrainMass Inc. brainmass.com October 5, 2022, 1:09 am ad1c9bdddf
    https://brainmass.com/math/algebra/inverse-function-451257

    SOLUTION This solution is FREE courtesy of BrainMass!

    a. Write an equation for the inverse function in the form of y=f^-1(x), b. graph f and f^-1 on the axes, and c. give the domain and the range of f and f^-1. If the function is not one-to-one, say so.

    1. y=4x-5
    Inverse function
    y = 4x - 5
    Change x as y and y as x,
    x = 4y - 5
    Write the y as function of x.
    4y = x + 5
    y = (x + 5)/4
    f^-1(x) = (x + 5)/4

    Graph

    Domain and Range
    y = 4x - 5
    Domain: Set of all real numbers
    Range: Set of all real numbers
    f^-1(x) = (x + 5)/4
    Domain: Set of all real numbers
    Range: Set of all real numbers

    Both the functions are linear, so they are one-to-one function.

    2. y=4/x
    Inverse function
    Change x as y and y as x,
    x = 4/y
    Write the y as function of x.
    y = 4/x
    f^-1(x) =4/x
    Both the f and f^(-1) are the same.
    Graph

    Domain and Range
    The function 4/x is not defined at x = 0.

    So domain: Set of all real numbers except zero
    Range: Set of all real numbers
    The function is one-to-one function.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com October 5, 2022, 1:09 am ad1c9bdddf>
    https://brainmass.com/math/algebra/inverse-function-451257

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