New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Functions question

2014 · Shift 1 · Q36

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Functions
2014 · Shift 1 · Q36

Functions question

2014 · Shift 1 · Q36

JEE AdvancedMathematicsFunctionsMultiple correct+3 / −1

Let

f:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R

be given by

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

. Then,

A
f(x) is an odd function
B
f(x) is a one-one function
C
f(x) is an onto function
D
f(x) is an even function

More from Functions

Let f1 : R $\to$ R, f2 : [0, $\infty$ ) $\to$ R, f3 : R $\to$ R, and f4 : R $\to$ [0, $\infty$ ) be defined by $f_{1} (x) = {∣ x ∣ e^{x} i f x < 0, i f x \geq 0;$ … Includes diagram2014 · MCQ
The function $f : [0, 3] \to [1, 29]$ , defined by $f (x) = 2 x^{3} - 15 x^{2} + 36 x + 1$ , is2012 · MCQ
Let $f : (- 1, 1) \to R$ be such that $f (cos 4 θ) = \frac{2}{2 - s e c ^{2} θ}$ for $θ \in (0, \frac{π}{4}) \cup (\frac{π}{4}, \frac{π}{2})$ . Then the value(s) of $f (\frac{1}{3})$ …2012 · Multiple correct
Let f(x) = x2 and g(x) = sin x for all x $\in$ R. Then the set of all x satisfying $(f \circ g \circ g \circ f) (x) = (g \circ g \circ f) (x)$ , where $(f \circ g) (x) = f (g (x))$ , is2011 · MCQ
Let $f : (0, 1) \to R$ be defined by $f (x) = \frac{b - x}{1 - b x}$ , where b is a constant such that $0 < b < 1$ . Then2011 · Multiple correct
Match the statements given in Column I with the intervals/union of intervals given in Column II : Includes diagram2011 · MCQ
Let $f, g$ and $h$ be real valued functions defined on the interval $f (x) = e^{x^{2}} + e^{- x^{2}}$ by $f (x) = e^{x^{2}} + e^{- x^{2}}$ , $g (x) = x e^{x^{2}} + e^{- x^{2}}$ and $h (x) = x^{2} e^{x^{2}} + e^{- x^{2}}$ . If $a, b$ and $c$ denote, respectively, the absolute maximum of $f, g$ and $h$ …2010 · MCQ
Let $S = {1, 2, 3, 4}$ . The total number of unordered pairs of disjoint subsets of $S$ is equal to :2010 · MCQ