Set, Relations and FunctionsMTP May 19 Series IIQuestion 1985 of 217
All Questions

A function f(x)\displaystyle f(x) is an even function, if

Options

A−f(x)=f(x)\displaystyle -f(x) = f(x)
Bf(−x)=f(x)\displaystyle f(-x) = f(x)
Cf(−x)=−f(x)\displaystyle f(-x) = -f(x)
Df(x)=−f(x)\displaystyle f(x) = -f(x)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — −f(x)=f(x)\displaystyle -f(x) = f(x)

All Options:

  • A−f(x)=f(x)\displaystyle -f(x) = f(x)
  • Bf(−x)=f(x)\displaystyle f(-x) = f(x)
  • Cf(−x)=−f(x)\displaystyle f(-x) = -f(x)
  • Df(x)=−f(x)\displaystyle f(x) = -f(x)

Detailed Solution & Explanation

By mathematical definition:
1. A function f(x)\displaystyle f(x) is an **even function** if:
f(−x)=f(x)∀xf(-x) = f(x) \quad \forall x
Examples include f(x)=x2\displaystyle f(x) = x^2, f(x)=cos⁡(x)\displaystyle f(x) = \cos(x). This corresponds to **Option B**.
2. A function f(x)\displaystyle f(x) is an **odd function** if:
f(−x)=−f(x)∀xf(-x) = -f(x) \quad \forall x
Examples include f(x)=x3\displaystyle f(x) = x^3, f(x)=sin⁡(x)\displaystyle f(x) = \sin(x). This corresponds to **Option C**.

**Discrepancy & Typographical Error:**
Mathematically, the definition of an even function is f(−x)=f(x)\displaystyle f(-x) = f(x), which is **Option B**. The textbook answer key (MTP May 19 Series II) contains a typographical error, designating **Option A** (−f(x)=f(x)\displaystyle -f(x) = f(x)) as correct. The mathematically correct definition is Option B.

Hence, **Option A** is the correct answer (according to the textbook key), but the mathematically proven correct value is f(−x)=f(x)\displaystyle f(-x) = f(x) (**Option B**).

More Questions from Set, Relations and Functions

If A={1,2,3,4,5}\displaystyle A = \{1, 2, 3, 4, 5\}, B={2,4}\displaystyle B = \{2, 4\} and C={1,3,5}\displaystyle C = \{1, 3, 5\} then (A−C)×B\displaystyle (A - C) \times B is:

If f(x)=x2−5\displaystyle f(x)=x^2-5, evaluate f(3)\displaystyle f(3), f(−4)\displaystyle f(-4), f(5)\displaystyle f(5), and f(1)\displaystyle f(1).

Out of a group of 20\displaystyle 20 teachers in a school, 10\displaystyle 10 teach Mathematics, 9\displaystyle 9 teach Physics and 7\displaystyle 7 teach Chemistry. 4\displaystyle 4 teach Mathematics and Physics but none teach both Mathematics and Chemistry. How many teach Chemistry and Physics; how many teach only Physics?

If A={1,2,3,4,5,7,8,9}\displaystyle A = \{1, 2, 3, 4, 5, 7, 8, 9\} and B={2,4,6,7,9}\displaystyle B = \{2, 4, 6, 7, 9\} then how many proper subset of A∩B\displaystyle A \cap B can be created?

The number of subsets of the set {0,1,2,3}\displaystyle \{0, 1, 2, 3\} is:

If f(x)=x2+x−1\displaystyle f(x) = x^2+x-1 and 4f(x)=f(2x)\displaystyle 4f(x) = f(2x), then find the value of 'x'.

Ready to Master Set, Relations and Functions?

Practice all 217 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free