Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 months ago

6. Suppose g(x) = 3+(x/2x-3).  Evaluate g^-1(-1)?

Precalc

9 Answers

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  • 4 months ago
    Favorite Answer

    Given: g(x) = 3 + (x / (2x - 3))

    Find the inverse, switch x and y and solve for y:

    x = 3 + (y / (2y - 3))

    x - 3 = y / (2y - 3)

    (2y - 3)(x - 3) = y

    2xy - 3x - 6y + 9 - y = 0

    2xy - 6y - y = 3x - 9

    y(2x - 7) = 3x - 9

    y = (3x - 9) / (2x - 7)

    g^-1(-1) = (3(-1) - 9) / (2(-1) - 7)

    g^-1(-1) = 4/3

  • 4 months ago

    Let g(x0 = y 

    Hence 

    y = 3 + (x / 2x - 3)) 

    Subtract '3' from both sides 

    y - 3 = x/(2x - 3)

    y(2x - 3) = x 

    2xy - 3y = x 

    2xy - x = 3y

    x(2y - 1) = 3y 

    x = 3y / (2y - 1)

    'Swop' the letters 

    y = 3x/(2x - 1) 

    g^-1(x) = 3x / (2x - 1) 

    g^-1(-1) = 3(-1) / (2(-1) - 1)

    g^-1(-1) = -3 / ( - 2 - 1) 

    g^-1(-1) = -3 / -3  = 3/3 = 1 

    Hence g^-1(-1) = 1 

  • 4 months ago

    (3 + x) / 2x

    That is the answer.

  • 4 months ago

    g(x) = 3 + x / ( 2x - 3 )

    y = 3 + x / ( 2x - 3 )

    ( y - 3 ) =  x / ( 2x - 3 )

    ( y - 3 )( 2x - 3 ) = x

    2xy - 6x - 3y + 9 = x

    x = 3( y - 3 ) / ( 2y - 7 )

    g⁻¹(x) = 3( x - 3 ) / ( 2x - 7 ), provided x ≠ 7/2

    g⁻¹(-1) = 3( -1 - 3 ) / ( 2(-1) - 7 )

    g⁻¹(-1) = 4/3

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  • Anonymous
    4 months ago

    its obvious. it spout 3,98.87645.54389.54. then it points west.

    dont forgrt! WEST! NOT NORTH NOT SOUTH! WEST!

    And finally when compared to dantes s(&)^c =°✓€ it makes a plausible evauation of the suns accelleration of 2/π>¥.

    pretty simple stuff.

  • 4 months ago

    g: y=3+[x/(2x-3)]

    =>

    g^-1: x=3+[y/(2y-3)]

    =>

    (x-3)(2y-3)=y

    =>

    (2x-7)y=3x-9

    =>

    y=3(x-3)/(2x-7)

    Thus,

    g^-1(-1)=3(-1-3)/(-2-7)

    =>

    g^-1(-1)=4/3.

  • Pope
    Lv 7
    4 months ago

    It probably is not what you intended, but you have defined g as a quadratic function.

    g(x) = 3+(x/2x-3)

    g(x) = 3 + (x²/2 - 3)

    g(x) = x²/2

    I am only taking you at your word. If you meant something else, then please review the order of operations and try again.

    Quadratic functions are not injective. Function g has no inverse.

  • 4 months ago

    Or you can just set g(x) to -1 and soslve for x:

    Presuming that is:

    g(x) = 3 + x / (2x - 3)  <-- see the difference?  that's not what you wrote

    We get:

    -1 = 3 + x / (2x - 3)

    -4 = x / (2x - 3)

    -4(2x - 3) = x

    -8x + 12 = x

    12 = 9x

    4/3 = x

    I get the same thing as Astrid.

  • rotchm
    Lv 7
    4 months ago

    Hint: As said previously, un-anon yourself and we will help you further. 

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