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Let f be any function defined on R and let it satisfy the condition :
|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈R
If f(0)=1, then
|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈R
If f(0)=1, then
- a)f(x)<0,∀ x∈R
- b)f(x) can take any value in R.
- c)f(x)>0,∀ x∈R
- d)f(x)=0,∀ x∈R
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Letfbe any function defined onRand let it satisfy the condition :|f(x)...
Is equal to |x - y| for all real x and y.
This means that the absolute value of the difference between f(x) and f(y) is always equal to the absolute value of the difference between x and y. In other words, the function f preserves the distance between any two real numbers.
One example of a function that satisfies this condition is the identity function f(x) = x. For any two real numbers x and y, |f(x) - f(y)| = |x - y|.
Another example is the function f(x) = -x. Again, for any two real numbers x and y, |f(x) - f(y)| = |-x - (-y)| = |-(x - y)| = |x - y|.
In general, any function of the form f(x) = ax + b, where a and b are real numbers, will satisfy the condition. This can be proven by substituting f(x) = ax + b and f(y) = ay + b into the given equation and simplifying.
Therefore, there are infinitely many functions that satisfy the given condition.
This means that the absolute value of the difference between f(x) and f(y) is always equal to the absolute value of the difference between x and y. In other words, the function f preserves the distance between any two real numbers.
One example of a function that satisfies this condition is the identity function f(x) = x. For any two real numbers x and y, |f(x) - f(y)| = |x - y|.
Another example is the function f(x) = -x. Again, for any two real numbers x and y, |f(x) - f(y)| = |-x - (-y)| = |-(x - y)| = |x - y|.
In general, any function of the form f(x) = ax + b, where a and b are real numbers, will satisfy the condition. This can be proven by substituting f(x) = ax + b and f(y) = ay + b into the given equation and simplifying.
Therefore, there are infinitely many functions that satisfy the given condition.
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Letfbe any function defined onRand let it satisfy the condition :|f(x)...
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Letfbe any function defined onRand let it satisfy the condition :|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈RIff(0)=1,thena)f(x)<0,∀ x∈Rb)f(x)can take any value inR.c)f(x)>0,∀ x∈Rd)f(x)=0,∀ x∈RCorrect answer is option 'C'. Can you explain this answer?
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Letfbe any function defined onRand let it satisfy the condition :|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈RIff(0)=1,thena)f(x)<0,∀ x∈Rb)f(x)can take any value inR.c)f(x)>0,∀ x∈Rd)f(x)=0,∀ x∈RCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Letfbe any function defined onRand let it satisfy the condition :|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈RIff(0)=1,thena)f(x)<0,∀ x∈Rb)f(x)can take any value inR.c)f(x)>0,∀ x∈Rd)f(x)=0,∀ x∈RCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Letfbe any function defined onRand let it satisfy the condition :|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈RIff(0)=1,thena)f(x)<0,∀ x∈Rb)f(x)can take any value inR.c)f(x)>0,∀ x∈Rd)f(x)=0,∀ x∈RCorrect answer is option 'C'. Can you explain this answer?.
Letfbe any function defined onRand let it satisfy the condition :|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈RIff(0)=1,thena)f(x)<0,∀ x∈Rb)f(x)can take any value inR.c)f(x)>0,∀ x∈Rd)f(x)=0,∀ x∈RCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Letfbe any function defined onRand let it satisfy the condition :|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈RIff(0)=1,thena)f(x)<0,∀ x∈Rb)f(x)can take any value inR.c)f(x)>0,∀ x∈Rd)f(x)=0,∀ x∈RCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Letfbe any function defined onRand let it satisfy the condition :|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈RIff(0)=1,thena)f(x)<0,∀ x∈Rb)f(x)can take any value inR.c)f(x)>0,∀ x∈Rd)f(x)=0,∀ x∈RCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Letfbe any function defined onRand let it satisfy the condition :|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈RIff(0)=1,thena)f(x)<0,∀ x∈Rb)f(x)can take any value inR.c)f(x)>0,∀ x∈Rd)f(x)=0,∀ x∈RCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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ample number of questions to practice Letfbe any function defined onRand let it satisfy the condition :|f(x)−f(y)|≤|(x−y)2|,∀ x,y∈RIff(0)=1,thena)f(x)<0,∀ x∈Rb)f(x)can take any value inR.c)f(x)>0,∀ x∈Rd)f(x)=0,∀ x∈RCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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