EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Functions>JEE Advanced Paper 1 - 2020>Q 4

HARD

JEE Advanced

IMPORTANT

Earn 100

If the function $f : R \to R$ is defined by $f (x) = |x| (x - \sin x)$ , then which of the following statements is TRUE?

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Important Questions on Functions

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Functions>JEE Advanced Paper 1 - 2015>Q 5

Let

f (x) = \sin (\frac{π}{6} \sin (\frac{π}{2} \sin x))

, for all

x \in R

and

g (x) = \frac{π}{2} \sin x

, for all

x \in R

. Let

(f o g) (x)

denote

f (g (x))

and

(g o f) (x)

denote

g (f (x))

. Then which of the following is (are) true?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Functions>JEE Advanced Paper 1 - 2014>Q 6

Let

f : (- \frac{π}{2}, \frac{π}{2}) \to R

be given by

f (x) = {(\log (\sec x + \tan x))}^{3} .

Then