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…

Question

let f 1 &#160; : R &#8594; R , &#160; f 2 &#160; : 0 , &#160; &#8734; &#8594; R , &#160; f 3 &#160; : R &#8594; R &#160; a n d &#160; f 4 &#160; : R &#8594; [ 0 , &#160; &#8734; ) be defined by f 1 x = x i f x &#60; 0 e x i f x &#8805; 0 &#160; ; f 2 x = x 2 ; f 3 x = sin &#8289; x i f x &#60; 0 x i f x &#8805; 0 &#160; a n d &#160; f 4 x = f 2 f 1 x i f x &#60; 0 f 2 f 1 x - 1 i f x &#8805; 0 List &ndash; I List &ndash; II (A) f 4 is (P) Onto but not one &ndash; 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

Aicharya · 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.

let f 1   : R → R ,   f 2   : 0 ,   ∞ → R ,   f 3   : R…

Solution

	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

let f 1 &#160; : R &#8594; R , &#160; f 2 &#160; : 0 , &#160; &#8734; &#8594; R , &#160; f 3 &#160; : R…

Solution

let f 1 : R → R , f 2 : 0 , ∞ → R , f 3 : R…