CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
A function is defined by f(x) = (x² − 4)/(x − 2) for x < 2, f(2) = a, and f(x) = b x − 2 for x > 2. If f is continuous at x = 2 and f(2) = a, what is the value of a + b?
The sum is 7, but check the options: none equals 7, so this item is flawed.
- A6Correct
- B4
- C5
- D8
Explanation
For x < 2, f(x) = x + 2, so the left-hand limit is 4. Continuity needs a = 4. The right-hand limit is 2b − 2, which must equal 4, so b = 3. Then a + b = 7. Checking: 2(3) − 2 = 4, correct, so the sum is 7, not 6.
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