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h asked in Science & MathematicsMathematics · 3 years ago

Calculus Help?

Suppose that f(x)=(x+1)/(x−1) is differentiable and has an inverse for x>1 and f(3)=2. Find (f^−1)′(2).

a)2

b)-2

c)-4

d)-1

e)4

pls help thanks!!

2 Answers

Relevance
  • ted s
    Lv 7
    3 years ago

    same as before f ' ( 3 ) = - 1 / 2 ====> inverse f(2) = - 2...(inv f )' (2) = 1 / [ f ' ( 3 ) ]

  • Ash
    Lv 7
    3 years ago

    f(x) = (x+1)/(x-1)

    To find inverse let f(x)=y

    y = (x+1)/(x-1)

    y(x-1)=x+1

    yx-y=x+1

    yx-x=y+1

    x(y-1)=y+1

    x = (y+1)/(y-1)

    switch x and y

    y = (x+1)/(x-1)

    f⁻¹(x) = (x+1)/(x-1)

    (f⁻¹)'(x) = [(x-1)-(x+1)]/(x-1)²

    (f⁻¹)'(x) = -2/(x-1)²

    (f⁻¹)'(2) = -2/(2-1)² = -2

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