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Consider a function f(x)=1-|x| on -1≤x≤1.The value of x at which the function attains a maximum, and the maximum value of function are:((mathematics:maxima,minima)
  • a)
    0, -1
  • b)
    -1, 0
  • c)
    0, 1
  • d)
    -1, 2
Correct answer is option 'C'. Can you explain this answer?
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Consider a function f(x)=1-|x| on -1≤x≤1.The value of x at which...
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Consider a function f(x)=1-|x| on -1≤x≤1.The value of x at which...
The function f(x) = 1 - |x| is defined for all real numbers x. However, you specified the interval -1 < x="" />< 1.="" in="" this="" interval,="" the="" function="" is="" given="" by="" f(x)="1" -="" />

To evaluate this function in the interval -1 < x="" />< 1,="" we="" first="" consider="" the="" absolute="" value="" of="" x.="" since="" x="" is="" restricted="" to="" the="" interval="" -1="" />< x="" />< 1,="" the="" absolute="" value="" of="" x="" will="" always="" be="" />

When x is positive, |x| = x. Therefore, f(x) = 1 - x for x > 0.

When x is negative, |x| = -x. Therefore, f(x) = 1 + x for x < />

In the interval -1 < x="" />< 1,="" x="" is="" positive,="" so="" f(x)="1" -="" />

Thus, the function f(x) = 1 - |x| on -1 < x="" />< 1="" simplifies="" to="" f(x)="1" -="" x.="" 1="" simplifies="" to="" f(x)="1" -="" />
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Consider a function f(x)=1-|x| on -1≤x≤1.The value of x at which the function attains a maximum, and the maximum value of function are:((mathematics:maxima,minima)a)0, -1b)-1, 0c)0, 1d)-1, 2Correct answer is option 'C'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a function f(x)=1-|x| on -1≤x≤1.The value of x at which the function attains a maximum, and the maximum value of function are:((mathematics:maxima,minima)a)0, -1b)-1, 0c)0, 1d)-1, 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a function f(x)=1-|x| on -1≤x≤1.The value of x at which the function attains a maximum, and the maximum value of function are:((mathematics:maxima,minima)a)0, -1b)-1, 0c)0, 1d)-1, 2Correct answer is option 'C'. Can you explain this answer?.
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