The function defined by g(x) = x ? [x] is discontinuous at:

Question

The function defined by $g (x) = x - [x]$ is discontinuous at:

Smart Achievers · Accepted Answer

(3)

Ans. all integral points

Explanation:

The function $f (x) = [x]$ is discontinuous at every integral point. Hence, the function $g (x) = x - [x]$ is also discontinuous at every integral point.

Solution

Q.
The function defined by $g (x) = x - [x]$ is discontinuous at:

1 all rational points

2 all irrational points

3 all integral points

4 None of the above

Ans.
(3)

Ans. all integral points

Explanation:

The function $f (x) = [x]$ is discontinuous at every integral point. Hence, the function $g (x) = x - [x]$ is also discontinuous at every integral point.

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