Relations and Functions (Class 11) · JEE Preparation Mathematics
For the function f: R → R defined by f(x) = x², which statement is correct?
Practice question from Relations and Functions (Class 11) (JEE Preparation Mathematics), with the correct answer and a step-by-step solution.
medium · MCQ · Q-D8F718
For the function f: R → R defined by f(x) = x², which statement is correct?
- A.f is one-one and onto.
- B.f is one-one but not onto.
- C.f is onto but not one-one.
- D.f is neither one-one nor onto.Correct answer
Solution
Since f(1) = f(-1), the function is not one-one. Its range is [0, ∞), which is not all of R, so it is not onto R either.
More from Relations and Functions (Class 11)
- Let A = {1, 2, 3}, B = {a, b}, and R = {(1, a), (2, b), (3, a)}. Which statement is correct?
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- Let f: R → R be defined by f(x) = (x − 1)² + 2. Find the range of f and state whether f is one-one.
- If A = {1, 2} and B = {a, b, c}, how many relations can be defined from A to B?
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