NTA Abhyas JEE Main2020MathematicsFunctionsPractice

The function f ( x ) = sec log x + 1 + x 2 is

Options

Aan odd function
Ban even function
Cneither an odd nor an even function
Da constant function

Correct answer

B. an even function

Step-by-step solution

f − x = sec log − x + 1 + x 2 = sec ⁡ log ⁡ x + 1 + x 2 - 1 ∵ 1 + x 2 - x = 1 1 + x 2 + x = sec − log x + 1 + x 2 = sec log x + 1 + x 2 ∵ sec − θ = sec θ = f ( x ) Hence f ( x ) is an even function.

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