If f(x) = 12, if x is an integer
- 7, if x is a real number which is not an integer
Find whether f is continuous at x = 9.
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It is given that
f(x) = 12 ; when x is an integer.
= -7; when x is not an integer.
f(9) = 12 (as 9 is an integer)
f(9-) = -7 (as 9- is something which is slightly less than 9, so it is not an integer)
f(9+) = -7 (as 9+ is something which is slightly more than 9, so it is not an integer)
Since f(9-) ≠ f(9) ≠ f(9+), f(x) is not continuous at x=9.
f(x) = 12 ; when x is an integer.
= -7; when x is not an integer.
f(9) = 12 (as 9 is an integer)
f(9-) = -7 (as 9- is something which is slightly less than 9, so it is not an integer)
f(9+) = -7 (as 9+ is something which is slightly more than 9, so it is not an integer)
Since f(9-) ≠ f(9) ≠ f(9+), f(x) is not continuous at x=9.
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