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Let f(x) = sgn (x) and g(x) = x (x2 – 5x + 6). The function f(g(x)) is discontinuous at
- a)Infinitely many points
- b)Exactly one point
- c)Exactly three points
- d)No point
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let f(x) = sgn (x) and g(x) = x (x2–5x + 6). The function f(g(x)...
Here's how to find g(f(x)):
First, we need to plug in f(x) into the expression for g(x):
g(x) = x(x^2 - 1)
g(f(x)) = f(x)(f(x)^2 - 1)
Since f(x) = sgn(x), we need to consider two cases: when x is positive and when x is negative.
Case 1: x > 0
When x is positive, f(x) = 1. So we have:
g(f(x)) = f(x)(f(x)^2 - 1) = 1(1^2 - 1) = 0
Case 2: x < />
When x is negative, f(x) = -1. So we have:
g(f(x)) = f(x)(f(x)^2 - 1) = -1((-1)^2 - 1) = 2
Therefore, g(f(x)) = 0 when x > 0 and g(f(x)) = 2 when x < 0.="" />
First, we need to plug in f(x) into the expression for g(x):
g(x) = x(x^2 - 1)
g(f(x)) = f(x)(f(x)^2 - 1)
Since f(x) = sgn(x), we need to consider two cases: when x is positive and when x is negative.
Case 1: x > 0
When x is positive, f(x) = 1. So we have:
g(f(x)) = f(x)(f(x)^2 - 1) = 1(1^2 - 1) = 0
Case 2: x < />
When x is negative, f(x) = -1. So we have:
g(f(x)) = f(x)(f(x)^2 - 1) = -1((-1)^2 - 1) = 2
Therefore, g(f(x)) = 0 when x > 0 and g(f(x)) = 2 when x < 0.="" />
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Community Answer
Let f(x) = sgn (x) and g(x) = x (x2–5x + 6). The function f(g(x)...
Given,
f(x)=sgn(x)
g(x)=x(x²-5x+6)
=>f(g(x))=sgn(x³-5x²+6x)
sgn(f(x)) is discontinuous whenever f(x) changes its sign.
x³-5x²+6x changes sign at three points: 0,2 and 3
So, f(g(x)) changes sign at three points.
Therefore, f(g(x)) is discontinuous at exactly three points.
Option (C)
f(x)=sgn(x)
g(x)=x(x²-5x+6)
=>f(g(x))=sgn(x³-5x²+6x)
sgn(f(x)) is discontinuous whenever f(x) changes its sign.
x³-5x²+6x changes sign at three points: 0,2 and 3
So, f(g(x)) changes sign at three points.
Therefore, f(g(x)) is discontinuous at exactly three points.
Option (C)
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Let f(x) = sgn (x) and g(x) = x (x2–5x + 6). The function f(g(x)) is discontinuous ata)Infinitely many pointsb)Exactly one pointc)Exactly three pointsd)No pointCorrect answer is option 'C'. Can you explain this answer?
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Let f(x) = sgn (x) and g(x) = x (x2–5x + 6). The function f(g(x)) is discontinuous ata)Infinitely many pointsb)Exactly one pointc)Exactly three pointsd)No pointCorrect answer is option 'C'. 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 f(x) = sgn (x) and g(x) = x (x2–5x + 6). The function f(g(x)) is discontinuous ata)Infinitely many pointsb)Exactly one pointc)Exactly three pointsd)No pointCorrect answer is option 'C'. 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 f(x) = sgn (x) and g(x) = x (x2–5x + 6). The function f(g(x)) is discontinuous ata)Infinitely many pointsb)Exactly one pointc)Exactly three pointsd)No pointCorrect answer is option 'C'. Can you explain this answer?.
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