Question

# If the function be such that $f\left(x\right)=x-\left[x\right]$, where [x] denotes the greatest integer less than or equal to x, then is (a) $\frac{1}{x-\left[x\right]}$ (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 $\ne$ Co-domain of f,  f is not onto. $⇒$ f is not a bijective function. So,  f -1 does not exist. Thus, the answer is (c).MathematicsRD Sharma XII Vol 1 (2015)Standard XII

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