CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
A function f is defined on the real numbers by f(x) = x² − 4x + 7. What is the range of f?
The range is [3, ∞). Writing f(x) = (x − 2)² + 3 shows the smallest value is 3 at x = 2, and the values increase without limit as x moves away from 2.
- AAll real numbers
- B[3, ∞)Correct
- C[7, ∞)
- D(−∞, 3]
Explanation
Complete the square: f(x) = (x − 2)² + 3. Since (x − 2)² ≥ 0, the minimum value is 3 at x = 2, and f grows without bound. Range is [3, ∞). Option C gives f(0), which is not the minimum.
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 A = {1, 2, 3, 4} and B = {2, 4, 6, 8}. A function f : A → B is defined as f(x) = 2x. How many elements are in the range of f?
- If A = {1, 2, {3, 4}}, which of the following statements is correct?
- The function f is defined by f(x) = (x² − 9)/(x − 3) for x ≠ 3 and f(3) = k. For what value of k is f continuous at x = 3?
- In a survey of 100 shareholders of a company, 60 hold equity shares, 45 hold preference shares and 15 hold neither. How many shareholders ho…
- In a group of 60 traders in a market, 35 deal in cloth, 28 deal in grain, and 8 deal in neither. How many traders deal in both cloth and gra…
- The function f(x) = 1/(x² − 25) is discontinuous at which of the following sets of points?