Let A = R : x ≥ 0\ . A function f : A → R^+ is defined by f(x) = x^2 . Which one of the following is correct? - Mathematics MCQ Mathematics Mock Test - 9 2026 | ExamTest.live

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Let A = {x \in R : x \geq 0} . A function f : A \to R^{+} is defined by f (x) = x^{2} . Which one of the following is correct?

Solution & Step-by-step Explanation

f (x) = x^{2} with domain [0, \infty) and codomain (0, \infty) .Injective: For x_{1}, x_{2} \in [0, \infty), x_{1}^{2} = x_{2}^{2} ⟹ x_{1} = x_{2} . It is one-one.Surjective: For every y \in (0, \infty), there exists x = y \in A . It is onto.Inverse f^{- 1} (y) = y . f (x) = x^{2} and f^{- 1} (x) = x .Since x^{2} \neq = x for all x, f is not its own inverse.

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Let A = {x \in R : x \geq 0} . A function f : A \to R^{+} is defined by f (x) = x^{2} . Which one of the following is correct?

The function does not have inverse

f is its own inverse

The function has an inverse but f is not its own inverse

None of the above

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