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Let f1 : R → R, 
and f4 : R → R, be functions defined by
where the inverse trigonometric function tan−1 x assumes values in 
denotes the greatest integer less than or equal to t,
The correct option is:
and f4 : R → R, be functions defined by where the inverse trigonometric function tan−1 x assumes values in denotes the greatest integer less than or equal to t,The correct option is:
- a)P → 2; Q →3; R →1; S→ 4
- b)P → 4; Q →1; R → 2; S→3
- c)P → 4; Q → 2; R →1; S→3
- d)P → 2; Q →1; R → 4; S→3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the...
(P)
The definition of function f1 is,
The continuity of function f1 is checked as follows.
It is clear that the function f1 is continuous at x = 0 and NOT differentiable at x = 0 .
Hence, for option (P), (2) is correct.
(Q)
The definition of function f2 is,
The continuity of function f2 is checked as follows.
It is clear from the above expression that the function f2 is NOT continuous at x = 0 .
Hence, for option (Q), (1) is correct.
(R)
The definition of function f3 is,
The continuity of function f2 is checked as follows.
From above expression, it is clear that, as x → 0 then, (x + 2) → 2 and thus, loge (x + 2) → loge2 and this is less than 1.
The range of function f3 can be expressed as,
The definition of function f3 can be written as,
The conclusion from the definition is,
Hence, for option (R), (4) is correct.
(S)
The definition of function f4 is,
The continuity of function f1 is checked as follows.
The definition of function f4 becomes.
It is clear that the function f4 is differentiable at x = 0 and its derivative is NOT continuous at x = 0 .
Hence, option (D) is correct.
The definition of function f1 is,
The continuity of function f1 is checked as follows.
It is clear that the function f1 is continuous at x = 0 and NOT differentiable at x = 0 .
Hence, for option (P), (2) is correct.
(Q)
The definition of function f2 is,
The continuity of function f2 is checked as follows.
It is clear from the above expression that the function f2 is NOT continuous at x = 0 .
Hence, for option (Q), (1) is correct.
(R)
The definition of function f3 is,
The continuity of function f2 is checked as follows.
From above expression, it is clear that, as x → 0 then, (x + 2) → 2 and thus, loge (x + 2) → loge2 and this is less than 1.
The range of function f3 can be expressed as,
The definition of function f3 can be written as,
The conclusion from the definition is,
Hence, for option (R), (4) is correct.
(S)
The definition of function f4 is,
The continuity of function f1 is checked as follows.
The definition of function f4 becomes.
It is clear that the function f4 is differentiable at x = 0 and its derivative is NOT continuous at x = 0 .
Hence, option (D) is correct.
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Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer?.
Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer?.
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Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let f1 : R→ R,andf4 : R→ R, be functions defined bywhere the inverse trigonometricfunction tan−1 x assumes values indenotes the greatest integer less than or equal to t,The correct option is:a)P → 2; Q →3; R →1; S→ 4b)P → 4; Q →1; R → 2; S→3c)P → 4; Q → 2; R →1; S→3d)P → 2; Q →1; R → 4; S→3Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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