Statement-1: The function F ( x )= x ln x is increasing in (1 / e , ∞) Statement-2: If f ( x ) and g ( x ) both are increasing in ( a , b ) then f ( x ) ⋅ g ( x ) must be increasing in ( a , b ).

Question

Statement-1: The function F ( x )= x ln x is increasing in (1 / e , ∞) Statement-2: If f ( x ) and g ( x ) both are increasing in ( a , b ) then f ( x ) ⋅ g ( x ) must be increasing in ( a , b ). (A) Statement-1 is true, statement- 2 is true and statement-2 is correct explanation for statement- 1 . (B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (C) Statement-1 is true, statement-2 is false. (D) Statement-1 is false, statement-2 is true.

Tardigrade Admin · Accepted Answer

f(x)=x and g(x)=x3 both are increasing in (-1,0) but h(x)=x ⋅ x3 is decreasing.

Q. Statement-1: The function $F (x) = x ln x$ is increasing in $(1/ e, \infty)$
Statement-2: If $f (x)$ and $g (x)$ both are increasing in $(a, b)$ then $f (x) \cdot g (x)$ must be increasing in $(a, b)$ .

Statement-1 is true, statement- 2 is true and statement-2 is correct explanation for statement- 1 .

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

Statement-1 is true, statement-2 is false.

Statement-1 is false, statement-2 is true.

$f (x) = x$ and $g (x) = x^{3}$ both are increasing in $(- 1, 0)$ but $h (x) = x \cdot x^{3}$ is decreasing.

Q. Statement-1: The function F(x)=xlnx is increasing in (1/e,∞) Statement-2: If f(x) and g(x) both are increasing in (a,b) then f(x)⋅g(x) must be increasing in (a,b).