JEE Advanced Model Paper 1 with solutions for online practice

f(x) = x2 - 2ax + a (a + 1)
Let y = f(x) = (x−a)2 + a , x ∊ [a , ∞)
Clearly y ≥ a
(x−a)2 = y - a
x = a + √y−a
f−1 (x) = a + √x−a
(x−a)2 + a = a + √x−a
∵ f(x) = f−1 (x)
⇒ x = a (or) (x−a)3 = 1
⇒ x = a (or) a + 1
If a = 5049 , then a + 1 = 5050
If a + 1 = 5049 , then a = 5048