Question

Consider the functions $f(x)=x-\sin x$ and $g(x)=x^4$.
Statement-1 : $f(x)$ is increasing for $x>0$ as well as $x<0$ and $g(x)$ is increasing for $x>0$ and decreasing for $x<0$.
Statement-2 : If an odd function is known to be increasing on the interval $x>0$ then it is increasing for $x<0$ also and if an even function is increasing for $x>0$ then it is decreasing for $x<0$.

• 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.

Answer 1

Answer: (A)

Correct answer is (a) Statement-1 is true, statement- 2 is true and statement-2 is correct explanation for statement- 1 .