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Given a real function f(x) = x if x does not belong to rational numbers 1-x if x belong to rational numbers THEN { . }= fractional part of x f({f({x})}) = 1 if x belong to integers {x- 1} if x does not belongs to integers?
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Given a real function f(x) = x if x does not belong to rational number...
Explanation:
Function f(x):
- The function f(x) is defined as x for x not belonging to rational numbers, and 1-x for x belonging to rational numbers.
f({f({x})}):
- When we apply the function f to the fractional part of x, denoted as {x}, we get 1 if x is an integer.
- If x is not an integer, we get the fractional part of (x-1).
Case 1: x is an integer:
- Let x = n, where n is an integer.
- f({n}) = f(0) = 1 (since the fractional part of an integer is 0)
- f({1}) = f(1) = 1
- Therefore, f({f({x})}) = f({1}) = 1
Case 2: x is not an integer:
- Let x = n + a, where n is an integer and a is a non-zero decimal part.
- f({n + a}) = f(a) = 1-a (since a is not a rational number)
- f({1-a}) = f(a) = 1-a
- Therefore, f({f({x})}) = f({1-a}) = 1-a
In conclusion, when x is an integer, f({f({x})}) = 1, and when x is not an integer, f({f({x})}) = 1 - a, where a is the non-zero decimal part of x.
Function f(x):
- The function f(x) is defined as x for x not belonging to rational numbers, and 1-x for x belonging to rational numbers.
f({f({x})}):
- When we apply the function f to the fractional part of x, denoted as {x}, we get 1 if x is an integer.
- If x is not an integer, we get the fractional part of (x-1).
Case 1: x is an integer:
- Let x = n, where n is an integer.
- f({n}) = f(0) = 1 (since the fractional part of an integer is 0)
- f({1}) = f(1) = 1
- Therefore, f({f({x})}) = f({1}) = 1
Case 2: x is not an integer:
- Let x = n + a, where n is an integer and a is a non-zero decimal part.
- f({n + a}) = f(a) = 1-a (since a is not a rational number)
- f({1-a}) = f(a) = 1-a
- Therefore, f({f({x})}) = f({1-a}) = 1-a
In conclusion, when x is an integer, f({f({x})}) = 1, and when x is not an integer, f({f({x})}) = 1 - a, where a is the non-zero decimal part of x.
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Given a real function f(x) = x if x does not belong to rational numbers 1-x if x belong to rational numbers THEN { . }= fractional part of x f({f({x})}) = 1 if x belong to integers {x- 1} if x does not belongs to integers?
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Given a real function f(x) = x if x does not belong to rational numbers 1-x if x belong to rational numbers THEN { . }= fractional part of x f({f({x})}) = 1 if x belong to integers {x- 1} if x does not belongs to integers? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Given a real function f(x) = x if x does not belong to rational numbers 1-x if x belong to rational numbers THEN { . }= fractional part of x f({f({x})}) = 1 if x belong to integers {x- 1} if x does not belongs to integers? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given a real function f(x) = x if x does not belong to rational numbers 1-x if x belong to rational numbers THEN { . }= fractional part of x f({f({x})}) = 1 if x belong to integers {x- 1} if x does not belongs to integers?.
Given a real function f(x) = x if x does not belong to rational numbers 1-x if x belong to rational numbers THEN { . }= fractional part of x f({f({x})}) = 1 if x belong to integers {x- 1} if x does not belongs to integers? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Given a real function f(x) = x if x does not belong to rational numbers 1-x if x belong to rational numbers THEN { . }= fractional part of x f({f({x})}) = 1 if x belong to integers {x- 1} if x does not belongs to integers? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given a real function f(x) = x if x does not belong to rational numbers 1-x if x belong to rational numbers THEN { . }= fractional part of x f({f({x})}) = 1 if x belong to integers {x- 1} if x does not belongs to integers?.
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