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Question

If the function f : RR be such that fx=x-x, where [x] denotes the greatest integer less than or equal to x, then f-1 x is

(a) 1x-x

(b) [x] − x

(c) not defined

(d) none of these


Solution

f(x) = x - [x]
We know that the range of f is [0, 1).
Co-domain of f = R
As range of f Co-domain of ff is not onto.
f is not a bijective function.
So,  f -1 does not exist.
Thus, the answer is (c).

Mathematics
RD Sharma XII Vol 1 (2015)
Standard XII

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