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Let f : [0, 1] → [–1, 1] and g : [–1, 1] → [0, 2] be two functions such that g is injective and gof : [0, 1] → [0, 2] is surjective. Then (A) f must be injective but need not be surjective (B) f must be surjective but need not be injective (C) f must be bijective (D) f must be a constant function |
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Answer» Correct option (B) f must be surjective but need not be injective Explanation: f : [0, 1] → [–1, 1] g : [1, 1] → [–0, 2] g is injective & gof is surjective. ⇒ f must be surjective otherwise f(x) would not cover the whole co-domain [–1, 1] (which is also the domain of g) & then consecutively gof would not be able to cover the whole [0, 2] (as g is injective). |
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