DIRECTIONS: This question contains two statements:
Statement-1 (Assertion) and Statement-2 (Reason).
This question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.
Let f(x)=(x+1)²−1, x≥−1
Statement-1: The set {x: f(x)=f⁻¹(x)

Question

DIRECTIONS: This question contains two statements:
Statement-1 (Assertion) and Statement-2 (Reason).
This question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.
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.

Accepted Answer

Statement-1 is true, Statement-2 is true. Statement-2 is not a correct explanation for Statement-1.. f is increasing, so f(x)=f^-1(x) reduces to f(x)=x: (x+1)^2-1=x -> x^2+x=0 -> x=0,-1, so St-1 is true. f is also a bijection onto its range [-1,inf), so St-2 is true, but being a bijection does not by itself produce the specific solution set, so it is not the correct explanation.

Solution

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