NTA Abhyas JEE Main2020MathematicsFunctionsPractice

Which of the following is a function whose graph is symmetrical about the origin?

Options

Af x = 2 x + 2 - x
Bf x = log ⁡ x + 1 + x 2 2
Cf x + y = f x + f y ∀ x , y ∈ R
DNone of these

Correct answer

C. f x + y = f x + f y ∀ x , y ∈ R

Step-by-step solution

A function whose graph is symmetrical about the origin must be odd. 2 x + 2 - x is an even function. Since, log ⁡ x + 1 + x 2 is an odd function, ∴ log ⁡ x + 1 + x 2 2 is an even function. If f x + y = f x + f y ∀ x , y ∈ R , then Put x = y = 0 ⇒ f 0 = 0 Now, put y = - x ⇒ f x + f - x = 0 ∴ f x is an odd function

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