Let f:R→R be defined as f(x)=[[ex],aex+[x−1],b+[sin(πx)],[e−x]−c,x<00≤x<11≤x<2x≥2
where a,b,c∈R and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?
Held on 28 Jun 2022 · Verified 6 Jul 2026.
There exists a,b,c∈R such that f is continuous of R.
If f is discontinuous at exactly one point, then a+b+c=1
If f is discontinuous at exactly one point, then a+b+c=1.
f is discontinuous at atleast two points, for any values of a,b and c.
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