The domain of $f (x)$ is $(0, 1)$ , then domain of $f (e^{x}) + f (\ln |x|)$ is

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Important Questions on Function

HARD

KVPY Aptitude Test - Stream SX

IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 2 - Function>EXERCISE>Q 25

If

f (x) = {(- 1)}^{[\frac{2 x}{π}]}, g (x) = |\sin x| - |\cos x|

and

ϕ (x) = f (x) g (x)

(where

[.]

denotes the greatest integer function), then the respective fundamental periods of

f (x), g (x)

and

ϕ (x)

are

MEDIUM

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Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 2 - Function>EXERCISE>Q 26

Let

f (x) = e^{\{e^{|x|} sgn x\}}

and

g (x) = e^{[e^{|x|} sgn x]}, x \in R

, where

\{.\}

and

[.]

denote the fractional and integral part functions, respectively. Also,

h (x) = \log (f (x)) + \log (g (x))

, then for real

x, h (x)

is

MEDIUM

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Practice Book for KVPY Aptitude Test - Stream SX Mathematics>Chapter 2 - Function>EXERCISE>Q 27

Let $f_{1} (x) = \{\begin{cases} x, & 0 \leq x \leq 1 \\ 1, & x > 1 \\ 0, & otherwise \end{cases}$ and $f_{2} (x) = f_{1} (- x)$ for all $x$ , $f_{3} (x) = - f_{2} (x)$ for all $x$ , $f_{4} (x) = f_{3} (- x)$ for all $x$ . Then which of the following is necessarily true?