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
