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JEE • MATHEMATICS • FUNCTIONS

Functions practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 31-33 of 33 questions

31 Hard

31 of 33

Application +4 | -1

Let the function

f\left( x \right) = 3{x^2} - 4x + 5\log \left( {1 + \left| x \right|} \right)

be defined on the interval

\left[ {0,1} \right].

The even extension of f(x) to the interval

\left[ { - 1,1} \right]

View answer and explanation

Correct option: A

3{x^2} + 4x + 8\log \left( {1 + \left| x \right|} \right)

The correct answer is A (

3{x^2} + 4x + 8\log ( {1 + \left| x \right|} )

) because the even extension involves replacing x with -x for negative values and simplifying.

32 Hard

32 of 33

Understanding +4 | -1

Let

f:R \to R

be a function defined by

f\left( x \right) = - \frac{{{{\left| x \right|}^3} + \left| x \right|}}{{1 + {x^2}}},

then the graph of

f\left( x \right)

lies in the

View answer and explanation

Correct option: D

III and IV quadrants

Option D (III and IV quadrants) is correct because the function

f(x)

is always negative or zero, causing its graph to lie in the third and fourth quadrants.

33 Hard

33 of 33

Analyzing +4 | -1

The domain of definition of

f\left( x \right) = {\log _{0.5}}\left\{ { - {{\log }_2}\left( {\frac{{3x - 1}}{{3x + 2}}} \right)} \right\},\;\mathrm{is}

View answer and explanation

Correct option: C

\left( {1/3,\infty } \right)

Option C ( (1/3, ∞) ) is correct because it satisfies the conditions for the logarithm to be defined, ensuring the arguments are positive.

Revision notes and key takeaways

Review FUNCTIONS in your textbook or class notes, then use this set to check your understanding.

Showing 31-33 of 33 questions

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