CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Which of the following functions defined on the set of real numbers is an even function?
The function f(x) = x⁴ + 3x² is even because f(−x) equals f(x), since both terms have even powers. The other functions are odd or neither, as x³ + x changes sign and x² + x and 2x + 1 do not satisfy either condition.
- Af(x) = x⁴ + 3x²Correct
- Bf(x) = x³ + x
- Cf(x) = x² + x
- Df(x) = 2x + 1
Explanation
A function is even if f(−x) = f(x). For x⁴ + 3x², replacing x by −x leaves it unchanged, so it is even. x³ + x is odd, while x² + x and 2x + 1 are neither even nor odd.
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} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Which of the following is correct?
- A set is given by A = {x : x is an integer and -2 < x ≤ 3}. How many elements does A have, and what is the sum of its elements?
- The domain of the real function f(x) = (2x − 3)/(x² − 5x + 6) is:
- Let f(x) = (x² − 16)/(x − 4) for x ≠ 4 and f(4) = 6. Which statement about f at x = 4 is correct?
- If f(x) = x² + 1 and g(x) = 3x − 2, what is the value of (f∘g)(2) − (g∘f)(2)?
- Let f(x) = 2x + 3. What is the inverse function f⁻¹(x)?