CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
The function f(x) = px + 3 for x ≤ 2, and f(x) = x² + q for x > 2, is continuous everywhere. If p = 4, what is the value of q?
q equals 7. At x = 2 the left piece gives 4(2) + 3 = 11, while the right piece tends to 4 + q. For continuity the two must be equal, so 4 + q = 11 and q = 7.
- A3
- B7Correct
- C−1
- D11
Explanation
Left-hand value at 2 is 4(2) + 3 = 11. Right-hand limit is 4 + q. Continuity needs 4 + q = 11, so q = 7. Choosing 3 or 11 comes from ignoring the x² term, and −1 from a sign error.
Did you get it right without looking?
One question tells you little. A timed set on Sets, Relations and Functions, Limits and Continuity shows your real accuracy, how long you take and where you lose marks.
More Sets, Relations and Functions, Limits and Continuity questions
- Let U = {1, 2, 3, ..., 12}, A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}. How many elements does (A ∪ B)' have, where the complement is ta…
- In a survey of 100 customers of a Pune store, 60 buy tea, 45 buy coffee and 20 buy both. How many customers buy neither tea nor coffee?
- A relation R is defined on the set of natural numbers as R = {(x, y) : x divides y}. Which of the following ordered pairs does NOT belong to…
- Let f(x) = (x² − 4x + 3)/(x − 1) for x ≠ 1. The value that must be assigned to f(1) so that f is continuous at x = 1 is:
- Consider a function f(x) = (x² − 9)/(x − 3). What is the value of lim(x → 3) f(x)?
- Let A = {1, 2, 3} and R = {(1,1), (2,2), (3,3), (1,2), (2,1)} be a relation on A. Which statement about R is correct?