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    Inverse of One-To-One Function Password GJVT

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    job morales
    Here are the steps to find the inverse of the given functions: 1. f x = 3x − 8 a) y = 3x − 8 b) x = 3y − 8 c) y = x/3 + 8/3 f^-1(x) = x/3 + 8/3 2. g x = x^2 − 6x − 7 a) y = x^2 − 6x − 7 b) x = y^2 − 6y − 7 c) y = x + 6 ± √(x + 6)^2 - 4(1)(−7) g^-1(x) = x + 6 ± √(

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    Inverse of One-To-One Function Password GJVT

    Uploaded by

    job morales
    13 views19 pages
    Here are the steps to find the inverse of the given functions: 1. f x = 3x − 8 a) y = 3x − 8 b) x = 3y − 8 c) y = x/3 + 8/3 f^-1(x) = x/3 + 8/3 2. g x = x^2 − 6x − 7 a) y = x^2 − 6x − 7 b) x = y^2 − 6y − 7 c) y = x + 6 ± √(x + 6)^2 - 4(1)(−7) g^-1(x) = x + 6 ± √(

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    Inverse of One-to-one Function Password GJVT

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    Here are the steps to find the inverse of the given functions: 1. f x = 3x − 8 a) y = 3x − 8 b) x = 3y − 8 c) y = x/3 + 8/3 f^-1(x) = x/3 + 8/3 2. g x = x^2 − 6x − 7 a) y = x^2 − 6x − 7 b) x = y^2 − 6y − 7 c) y = x + 6 ± √(x + 6)^2 - 4(1)(−7) g^-1(x) = x + 6 ± √(

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    13 views19 pages

    Inverse of One-To-One Function Password GJVT

    Uploaded by

    job morales
    Here are the steps to find the inverse of the given functions: 1. f x = 3x − 8 a) y = 3x − 8 b) x = 3y − 8 c) y = x/3 + 8/3 f^-1(x) = x/3 + 8/3 2. g x = x^2 − 6x − 7 a) y = x^2 − 6x − 7 b) x = y^2 − 6y − 7 c) y = x + 6 ± √(x + 6)^2 - 4(1)(−7) g^-1(x) = x + 6 ± √(

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 19

    INVERSE OF

    ONE-TO-ONE
    FUNCTION
    Original Function
    x -4 -3 -2 -1 0 1 2 3 4
    y -9 -7 -5 -3 -1 1 3 5 7

    Inverse Function
    x -9 -7 -5 -3 -1 1 3 5 7
    y -4 -3 -2 -1 0 1 2 3 4
    Example

    Find the inverse of the function


    describe by the set of ordered pairs.
    {(1,-3), (2,1), (3,3), (4,5,), (5,7}

    Solution
    {(-3,1), (1,2), (3,3), (5,4,), (7,5}
    Example

    Find the inverse of the function


    𝒇 𝒙 = 𝟑𝒙 + 𝟏
    To find the inverse of one-to-one function

    A. Write the function in the form of


    𝑦=𝑓 𝑥 .
    B. Interchange the 𝑥 and 𝑦 variables.
    C. Solve for 𝑦 in terms of 𝑥
    Example Find the inverse of the function 𝒇 𝒙 = 𝟑𝒙 + 𝟏

    A. Write the function in the form of 𝑦 = 𝑓 𝑥 .

    𝒇 𝒙 = 𝟑𝒙 + 𝟏
    𝒚 = 𝟑𝒙 + 𝟏
    Example Find the inverse of the function 𝒇 𝒙 = 𝟑𝒙 + 𝟏

    B. Interchange the 𝑥 and 𝑦 variables.

    𝒚 = 𝟑𝒙 + 𝟏
    𝒙 = 𝟑𝒚 + 𝟏
    Example Find the inverse of the function 𝒇 𝒙 = 𝟑𝒙 + 𝟏

    C. Solve for 𝑦 in terms of 𝑥


    𝒙 = 𝟑𝒚 + 𝟏
    −𝟑𝒚 + 𝒙 = 𝟏
    −𝟑𝒚 = −𝒙 + 𝟏 𝒙−𝟏
    𝒚=
    −𝟑𝒚 −𝒙 + 𝟏 𝟑
    =
    −𝟑 −𝟑
    −𝒙 + 𝟏 Since the inverse of the
    𝒚= function is denoted by 𝒇−𝟏,
    −𝟑
    −(𝒙 − 𝟏) 𝒙−𝟏
    𝒚= 𝑓 −1
    (𝑥) =
    −𝟑 𝟑
    EXAMPLE 2: Find the inverse of 𝒈 𝒙 = 𝒙 − 𝟐 𝟑

    A. Write the function in the form of 𝑦 = 𝑓 𝑥 .

    𝟑
    𝒈 𝒙 = −𝟐 𝒙
    𝟑
    𝒚=𝒙 −𝟐
    EXAMPLE 2: Find the inverse of 𝒈 𝒙 = 𝒙 − 𝟐
    𝟑

    B. Interchange the 𝑥 and 𝑦 variables.


    𝟑
    𝒚=𝒙 −𝟐
    𝟑
    𝒙=𝒚 −𝟐
    EXAMPLE 2: Find the inverse of 𝒈 𝒙 = 𝒙 − 𝟐 𝟑

    C. Solve for 𝑦 in terms of 𝑥


    𝒙= −𝟐 𝒚 𝟑
    𝒚𝟑 = 𝒙 + 𝟐
    𝟑
    −𝒚 + 𝒙 = −𝟐 𝟑 𝟑
    𝟑
    𝒚 = 𝒙+𝟐
    𝟑
    −𝒚 = −𝟐 − 𝒙
    𝟑
    −𝒚 𝟑 −𝒙 − 𝟐 𝒚= 𝒙+𝟐
    = Since the inverse of the
    −𝟏 −𝟏 function is denoted by 𝒇−𝟏,
    −𝒚 𝟑 −(𝒙 + 𝟐)
    = −𝟏
    𝒈 (𝒙) =
    𝟑
    𝒙+𝟐
    −𝟏 −𝟏
    𝟐𝒙+𝟏
    EXAMPLE 3: Find the inverse of 𝒇 𝒙 =
    𝟑𝒙−𝟒

    A. Write the function in the form of 𝑦 = 𝑓 𝑥 .


    𝟐𝒙 + 𝟏
    𝒇 𝒙 =
    𝟑𝒙 − 𝟒
    𝟐𝒙 + 𝟏
    𝒚=
    𝟑𝒙 − 𝟒
    𝟐𝒙+𝟏
    EXAMPLE 3: Find the inverse of 𝒇 𝒙 =
    𝟑𝒙−𝟒

    B. Interchange the 𝑥 and 𝑦 variables.


    𝟐𝒙 + 𝟏
    𝒚=
    𝟑𝒙 − 𝟒
    𝟐𝒚 + 𝟏
    𝒙=
    𝟑𝒚 − 𝟒
    𝟐𝒙+𝟏
    EXAMPLE 3: Find the inverse of 𝒇 𝒙 =
    𝟑𝒙−𝟒

    C. Solve for 𝑦 in terms of 𝑥


    𝟐𝒚 + 𝟏 𝒚(𝒙 − 𝟐) 𝟒𝒙 + 𝟏
    𝒙= =
    𝟑𝒚 − 𝟒 𝒙−𝟐 𝒙−𝟐
    𝒙 𝟑𝒚 − 𝟒 = 𝟐𝒚 + 𝟏 𝟒𝒙 + 𝟏
    𝒚=
    𝒙−𝟐
    𝟑𝒙𝒚 − 𝟒𝒙 = 𝟐𝒚 + 𝟏
    𝟑𝒙𝒚 = 𝟐𝒚 + 𝟒𝒙 + 𝟏 𝟒𝒙 + 𝟏
    𝒇−𝟏 (𝒙) =
    𝟑𝒙𝒚 − 𝟐𝒚 = 𝟒𝒙 + 𝟏 𝒙−𝟐
    𝒚(𝒙 − 𝟐) = 𝟒𝒙 + 𝟏
    EXAMPLE 4: Find the inverse of 𝒇 𝒙 = 𝒙𝟐 + 𝟒𝒙 − 𝟐

    It is not a one-to-
    one function
    EXAMPLE 4: Find the inverse of 𝒇 𝒙 = |𝒙|

    It is not a one-to-
    one function
    PRACTICE EXERCISE

    Find the inverse of the given function.

    1.𝑓 𝑥 = 3𝑥 − 8
    2
    2.𝑔 𝑥 = 𝑥 − 6𝑥 − 7
    4𝑥+2
    3.ℎ 𝑥 = 𝑥−3

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