demauryobispo09
Answered

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f(x)=2x+1/x-1 then f^-1(1)​

Sagot :

mhanifa

Answer:

  • f⁻¹(x) = (x + 1) / (x - 2)
  • f⁻¹(1 ) = - 2

Step-by-step explanation:

Given function:

  • f(x) = (2x + 1) / (x - 1)

Find its inverse, substitute x with y and f(x) with x, solve for y:

  • x = (2y + 1) / (y - 1)
  • x(y - 1) = 2y + 1
  • xy - x = 2y + 1
  • xy - 2y = x + 1
  • y(x - 2) = x + 1
  • y = (x + 1) / (x - 2)

Substitute y with f⁻¹(x):

  • f⁻¹(x) = (x + 1) / (x - 2)

Find  f⁻¹(1 ):

  • f⁻¹(1 ) = ( 1 + 1) / (1 - 2) = 2 / - 1 = - 2
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