Let {\f}: {\R} \to {\R} be defined as f(x)=[\table {[e^x],} , x< 0 ; {a e^x+[x-1],} , 0 \leq x< 1 ; {b+[\sin (\pi x)],} , 1 \leq x< 2 ; {[e^{-x}]-c,} , x \geq 2 . where a, b, c \in R and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true? [28-Jun-2022-Shift-1]

Correct Answer is : If f is discontinuous at exactly one point, then a+b+c≠1

There exists a, b, c \in R such that f is continuous on {\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 \neq 1

f is discontinuous at at least two points, for any values of a, b and c

Limits, Continuity and Differentiability Part 2

Section: Mathematics

Question : 38 of 100

Marks: +1, -0

Let f:R→R be defined as
f(x)=[

where a,b,c∈R and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?

[28-Jun-2022-Shift-1]

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