let f 1 : R → R , f 2 : 0 , ∞ → R , f 3 : R → R a n d f 4 : R → [ 0 , ∞ ) be defined by f 1 x = x i f x

Question

let f 1 : R → R , f 2 : 0 , ∞ → R , f 3 : R → R a n d f 4 : R → [ 0 , ∞ ) be defined by f 1 x = x i f x < 0 e x i f x ≥ 0 ; f 2 x = x 2 ; f 3 x = sin ⁡ x i f x < 0 x i f x ≥ 0 a n d f 4 x = f 2 f 1 x i f x < 0 f 2 f 1 x - 1 i f x ≥ 0 List – I List – II (A) f 4 is (P) Onto but not one – one (B) f 3 is (Q) neither continuous nor one-one (C) f 2 of f 1 is (R) differentiable but not one-one (D) f 2 is (S) continuous and one-one

TestHub · Accepted Answer

f 2 f 1 = x 2 , x < 0 e 2 x , x ≥ 0 f 4 : R → [ 0 , ∞ ) f 4 x = f 2 f 1 x , x < 0 f 2 f 1 x - 1 , x ≥ 0 = x 2 , x < 0 e 2 x - 1 , x ≥ 0 f 2 x is continuous and one-one. f 3 x is differentiable but not one-one. f 2 f 1 x is neither one one nor continuous. f 4 x is onto but not one-one.

Mathematics - Functions Question with Solution | TestHub

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Doubts & Discussion

	List – I		List – II
(A)	$f_{4}$ is	(P)	Onto but not one – one
(B)	$f_{3}$ is	(Q)	neither continuous nor one-one
(C)	$f_{2}$ of $f_{1}$ is	(R)	differentiable but not one-one
(D)	$f_{2}$ is	(S)	continuous and one-one