JEE 2023 Mathematics PYQ — Let be defined by: where is the greatest integer function. Find w… | Mathem Solvex | Mathem Solvex
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JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023
Let f:(−2,2)→R be defined by: f(x)={x[x],(x−1)[x],amp;−2amp;0≤xlt;xlt;2lt;0where [x] is the greatest integer function. Find m+n where m is points of non-continuity and n is points of non-differentiability.
Choose the correct answer:
A.
4
(Correct Answer)
B.
3
C.
2
D.
1
Correct Answer:
4
Explanation
Let f:(−2,2)→R be defined by: f(x)={x[x],(x−1)[x],amp;−2amp;0≤xlt;xlt;2lt;0 Breaking the function into intervals: f(x)=⎩⎨⎧x(−2)=−2x,x(−1)=−x,(x−1)(0)=0,(x−1)(1)=x−1,amp;−2amp;−1≤xamp;0≤xamp;1≤xlt;xlt;0lt;1lt;2lt;−1
from the graph, its clear that f(x) is discontinous at 1 point and non differentiable at 3 points So m = 1 and n = 3 and m + n = 4
Explanation
Let f:(−2,2)→R be defined by: f(x)={x[x],(x−1)[x],amp;−2amp;0≤xlt;xlt;2lt;0 Breaking the function into intervals: f(x)=⎩⎨⎧x(−2)=−2x,x(−1)=−x,(x−1)(0)=0,(x−1)(1)=x−1,amp;−2amp;−1≤xamp;0≤xamp;1≤xlt;xlt;0lt;1lt;2lt;−1
from the graph, its clear that f(x) is discontinous at 1 point and non differentiable at 3 points So m = 1 and n = 3 and m + n = 4
