Q80.If f(x) + 2f( x1 ) = 3x, x ≠0, and S = {x ∈R : f(x) = f(−x)}, then S (1) Contains exactly two elements (2) Contains more than two elements (3) Is an empty set (4) Contains exactly one element
What This Question Tests
This question requires solving a functional equation to determine the explicit form of f(x) and then applying the definition of an even function, f(x) = f(-x), to find the elements in the specified set S.
Concepts Tested
📚 NCERT Sections This Tests
1.1 — Define The Term Solution. How Many Types Of Solutions Are Formed? Write Briefly
Chemistry Class 11 · Chapter 1
1.1 Define the term solution. How many types of solutions are formed? Write briefly about each type with an example.
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
📋 Question Details
- Chapter
- Sets Relations Functions
- Topic
- Functional equations, even functions
- Year
- 2016
- Shift
- 03 Apr
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 2: Relations and Functions
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