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The function f(x) is defined by f(x) = 
- a)Is continuous at x = 1
- b)Is discontinuous at x = 1 since f(1+) does not exist though f(1_) exists
- c)Is discontinuous at x = 1 since f(1_) does not exist though f(1+) exists
- d)Is discontinuous since neither f(1_) nor f(1+) exists.
Correct answer is option 'D'. Can you explain this answer?
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The function f(x) is defined by f(x) =a)Is continuous at x = 1b)Is dis...
Because log fuction can not contain 1 in the base because When you have a power function with base 0, the result of that power function is always going to be 0. ... And if those numbers Can't reliably be the base of a power function, then they also Can't reliably be the base of a logarithm. For that reason, we only allow positive numbers other than 1 as the base of the logarithm.
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The function f(x) is defined by f(x) =a)Is continuous at x = 1b)Is dis...
lt x1^+ f(x) = log(4x -3) (x2- 2x + 5)
= ln(x2 - 2x +5)/ln(4x-3)
lt(h → 0) ln(1+h)2 - 2(1+h) + 5)/ln(4(1+h) - 3)
lt(h → 0) ln(1+h2 + 2h - 2 -2h + 5)/ln(4 + 4h - 3)
ln(h → 0) ln(4 + h2)/(1+4h)
Divide and multiply the denominator by 4h
ln(h → 0) ln(4 + h2)/[((1+4h)/4h) * 4h]
As we know that (1+4h)/4h = 1
ln 4/(4*0) = + ∞ (does not exist)
lt x→ 1^- f(x) = log(4x -3) (x2- 2x + 5)
lt(h → 0) ln(1-h)2 - 2(1-h) + 5)/ln(4(1-h) - 3)
lt(h → 0) ln(1+h2 - 2h - 2 + 2h + 5)/ln(4 - 4h - 3)
ln(h → 0) ln(4 + h2)/(1 - 4h)
Divide and multi[ly the denominator by (-4h)
ln(h → 0) ln(4 + h2)/[((1+4h)/-4h) * (-4h)
As we know that (1-4h)/(-4h) = 1
ln 1/(-4*0) = - ∞ (does not exist)
= ln(x2 - 2x +5)/ln(4x-3)
lt(h → 0) ln(1+h)2 - 2(1+h) + 5)/ln(4(1+h) - 3)
lt(h → 0) ln(1+h2 + 2h - 2 -2h + 5)/ln(4 + 4h - 3)
ln(h → 0) ln(4 + h2)/(1+4h)
Divide and multiply the denominator by 4h
ln(h → 0) ln(4 + h2)/[((1+4h)/4h) * 4h]
As we know that (1+4h)/4h = 1
ln 4/(4*0) = + ∞ (does not exist)
lt x→ 1^- f(x) = log(4x -3) (x2- 2x + 5)
lt(h → 0) ln(1-h)2 - 2(1-h) + 5)/ln(4(1-h) - 3)
lt(h → 0) ln(1+h2 - 2h - 2 + 2h + 5)/ln(4 - 4h - 3)
ln(h → 0) ln(4 + h2)/(1 - 4h)
Divide and multi[ly the denominator by (-4h)
ln(h → 0) ln(4 + h2)/[((1+4h)/-4h) * (-4h)
As we know that (1-4h)/(-4h) = 1
ln 1/(-4*0) = - ∞ (does not exist)
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The function f(x) is defined by f(x) =a)Is continuous at x = 1b)Is discontinuous at x = 1 since f(1+) does not exist though f(1_) existsc)Is discontinuous at x = 1 since f(1_) does not exist though f(1+) existsd)Is discontinuous since neither f(1_) nor f(1+) exists.Correct 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 The function f(x) is defined by f(x) =a)Is continuous at x = 1b)Is discontinuous at x = 1 since f(1+) does not exist though f(1_) existsc)Is discontinuous at x = 1 since f(1_) does not exist though f(1+) existsd)Is discontinuous since neither f(1_) nor f(1+) exists.Correct 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 The function f(x) is defined by f(x) =a)Is continuous at x = 1b)Is discontinuous at x = 1 since f(1+) does not exist though f(1_) existsc)Is discontinuous at x = 1 since f(1_) does not exist though f(1+) existsd)Is discontinuous since neither f(1_) nor f(1+) exists.Correct answer is option 'D'. Can you explain this answer?.
The function f(x) is defined by f(x) =a)Is continuous at x = 1b)Is discontinuous at x = 1 since f(1+) does not exist though f(1_) existsc)Is discontinuous at x = 1 since f(1_) does not exist though f(1+) existsd)Is discontinuous since neither f(1_) nor f(1+) exists.Correct 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 The function f(x) is defined by f(x) =a)Is continuous at x = 1b)Is discontinuous at x = 1 since f(1+) does not exist though f(1_) existsc)Is discontinuous at x = 1 since f(1_) does not exist though f(1+) existsd)Is discontinuous since neither f(1_) nor f(1+) exists.Correct 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 The function f(x) is defined by f(x) =a)Is continuous at x = 1b)Is discontinuous at x = 1 since f(1+) does not exist though f(1_) existsc)Is discontinuous at x = 1 since f(1_) does not exist though f(1+) existsd)Is discontinuous since neither f(1_) nor f(1+) exists.Correct answer is option 'D'. Can you explain this answer?.
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