Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 1 - Relations & Functions>Exercise 2>Q 20

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The domain of $f (x) = \sqrt{\cos (\sin x)} + \sqrt{\log_{x} \{x\}}; \{\cdot\}$ denotes the fractional part, is

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Important Questions on Relations & Functions

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 1 - Relations & Functions>Exercise 2>Q 21

If

R

be a relation from

A = {1, 2, 3, 4}

to

B = {1, 3, 5}

such that

(a, b) \in R \Leftrightarrow a < b

, then

R O R^{- 1}

is

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 1 - Relations & Functions>Exercise 2>Q 22

The least value of

x

for which

f (x) = \frac{\sqrt{x^{2} - 4}}{\sin^{- 1} (2 - x)}

is defined is

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IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 1 - Relations & Functions>Exercise 2>Q 23

f (x) = \frac{\cos x}{[\frac{x}{π}] + \frac{1}{2}},

where

x

is not an integral multiple of

π

and

[x]

denote the greatest integer function, is

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IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 1 - Relations & Functions>Exercise 2>Q 24

Let

f (x) = \frac{\sin x}{\sqrt{1 + \tan^{2} x}} - \frac{\cos x}{\sqrt{1 + \cot^{2} x}}

. Then range of

f (x)

is

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 1 - Relations & Functions>Exercise 2>Q 25

If

f (x) = \frac{1 - x}{1 + x}; x \neq - 1, 0

, and

x > 0

then

f [f (x)] + f [f (\frac{1}{x})]

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 1 - Relations & Functions>Exercise 2>Q 26

If

3 f (x) - f (\frac{1}{x}) = \log_{e} x^{4},

the

f (e^{- x})

is

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Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 1 - Relations & Functions>Exercise 2>Q 27

The function $f (x) = \frac{x}{e^{x} - 1} + \frac{x}{2} + 1$ is