JAMIA 2022 — Mathematics PYQ
JAMIA | Mathematics | 2022The function f(x) is defined in (-5, 5) as f(x) = {x,−x,amp;if x∈Qamp;if x∈/Q
Choose the correct answer:
- A.
f(x) is continuous at every x, except x = 0
- B.
f(x) is discontinuous at every x, except x = 0
(Correct Answer) - C.
f(x) is continuous everywhere
- D.
f(x) is discontinuous everywhere
f(x) is discontinuous at every x, except x = 0
Explanation
For the function f(x)={x,−x,amp;x∈Qamp;x∈/Q:
Continuity Analysis
f(x) is continuous at a if and only if:
limx→a,x∈Qf(x)=limx→a,x∈/Qf(x)
a=−a
2a=0⟹a=0
Conclusion
-
At x=0: Continuous
-
At x=0: Discontinuous
Result: f(x) is discontinuous at every x except x=0.
Explanation
For the function f(x)={x,−x,amp;x∈Qamp;x∈/Q:
Continuity Analysis
f(x) is continuous at a if and only if:
limx→a,x∈Qf(x)=limx→a,x∈/Qf(x)
a=−a
2a=0⟹a=0
Conclusion
-
At x=0: Continuous
-
At x=0: Discontinuous
Result: f(x) is discontinuous at every x except x=0.