Question

Let f(x) = (x + 1)2 -1, x ≥ -1

Statement -1: The set {x:f(x) = f-1(x)}= {0,-1}

Statement -2: f is a bijection.

(A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

(B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

(C) Statement-1 is true, Statement-2 is false

(D) Statement-1 is false, Statement-2 is true

Answer 1

Correct option**(C) Statement-1 is true, Statement-2 is false**

Explanation :

From Fig, f is one-one in [−1,∞) . There is no information about co-domain and therefore f(x) is not necessarily onto function. Therefore, S1 is true but S2 is false.