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 1>Q 23

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The function $f : [2, \infty) \to (0, \infty)$ defined by $f (x) = x^{2} - 4 x + a,$ then the set of values of $a$ for which $f (x)$ becomes onto is

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Important Questions on Relations & Functions

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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 1>Q 24

If

f : R \to R, f (x) = \{\begin{cases} x | x | - 4, & x \in Q \\ x | x | - \sqrt{3} & x \notin Q \end{cases},

then

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 1>Q 25

If

f (x) = |x|

and

g (x) = [x],

then value of

fog (- \frac{1}{4}) + gof (- \frac{1}{4})

is, where

[\cdot]

denotes the greatest integer function

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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 1>Q 26

The domain of the functions

f (x) = \log_{2} \log_{3} \log_{4} 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 1>Q 27

Domain of

\cos^{- 1} [2 x^{2} - 3],

where

[\cdot]

denotes greatest integer function 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 1>Q 28

If

f (x) = \ln (\frac{x^{2} + e}{x^{2} + 1}),

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 1>Q 29

The function

y (x)

given implicitly by

3 \sin y + a \sin x = 1, a > 0

exists provided, then

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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 1>Q 30

The function

y (x)

given implicitly by the equation

3 \sin y + 5 \sin x = 1

is real in

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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 1>Q 31

The domain and range of the function

f

given by

f (x) = 2 - |x - 5|

is