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(x-[x])/(1-[x]+x) find the values of x satisfying or find range

(x-[x])/(1-[x]+x) find the values of x satisfying or find range

Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
4 years ago
hello sahil your question is not clear as to what you mean by “find the values of x satisfying”?
however, i can find the range for you:
we know that x= [x]+{x}
now, y= (x-[x])/(1-[x]+x) can be written as
y= {x}/(1+{x})= 1 – 1/(1+{x})
now we know that {x} lies in [0, 1).
so that 1 + {x} lies in [1, 2).
or 1/(1 + {x}) lies in (1/2, 1].
or – 1/(1 + {x}) lies in [ – 1, – 1/2).
or 1 – 1/(1 + {x}) lies in [0, 1/2).
so, range of y= (x-[x])/(1-[x]+x) is [0, 1/2).
kindly approve

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