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A function f(x) is defined by f(x) = (x–2)+1 over all real values of x. now f(x) is
- a)Continuous at x = 2
- b)Discontinuous at x = 2
- c)Undefined at x = 2
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A function f(x) is defined by f(x) = (x–2)+1 over all real value...
Explanation:
The given function is f(x) = (x^2)^(1/2) = |x| for all real values of x.
Continuity of a function at a point:
A function is said to be continuous at a point if the limit of the function at the point exists and is equal to the value of the function at that point.
Determining continuity of f(x) at x = 2:
Let us consider the left-hand limit and right-hand limit of the function at x = 2.
Left-hand limit:
lim x→2− f(x) = lim x→2− |x| = lim x→2− −x = −2
Right-hand limit:
lim x→2+ f(x) = lim x→2+ |x| = lim x→2+ x = 2
As the left-hand limit and the right-hand limit are not equal, the limit of the function does not exist at x = 2.
Therefore, the function is not continuous at x = 2.
Conclusion:
The correct option is (A) Continuous at x = 2.
The given function is f(x) = (x^2)^(1/2) = |x| for all real values of x.
Continuity of a function at a point:
A function is said to be continuous at a point if the limit of the function at the point exists and is equal to the value of the function at that point.
Determining continuity of f(x) at x = 2:
Let us consider the left-hand limit and right-hand limit of the function at x = 2.
Left-hand limit:
lim x→2− f(x) = lim x→2− |x| = lim x→2− −x = −2
Right-hand limit:
lim x→2+ f(x) = lim x→2+ |x| = lim x→2+ x = 2
As the left-hand limit and the right-hand limit are not equal, the limit of the function does not exist at x = 2.
Therefore, the function is not continuous at x = 2.
Conclusion:
The correct option is (A) Continuous at x = 2.
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Community Answer
A function f(x) is defined by f(x) = (x–2)+1 over all real value...
F(x) = x - 1
f(2) = 2-1 = 1
hence continuous
f(2) = 2-1 = 1
hence continuous
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A function f(x) is defined by f(x) = (x–2)+1 over all real values of x. now f(x) isa)Continuous at x = 2b)Discontinuous at x = 2c)Undefined at x = 2d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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