Question

F(x)=2x+1/x-1 then f^-1(1)​

Answer 1

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

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