UPSEE Solved Model Paper 7

Given :
f (x) =

2x−1

x+5

(x ≠ - 5)
We have to find f−1(x)
Let y = f (x) =

2x−1

x+5

⇒ y (x + 5) = 2x - 1
⇒ xy + 5y = 2x - 1
⇒ x (y - 2) = - 1 - 5y
⇒ x =

−(1+5y)

−(2−y)

⇒ x =

1+5y

2−y

∴ f−1 x =

1+5x

2−x

, (x ≠ 2) [Using definition of inverse of function]
Hence, option 'D' is correct.