Which-of-the-following-is-an-even-function-A-f-1-x-sin-x-3-x-3-x-B-f-2-x-cos-x-3-x-3-x-C-f-3-x-log-10-x-x-2-1-D-f-4-x-x-2-10-x-1-

Question Number 165808 by ZiYangLee last updated on 08/Feb/22

Which of the following is an even function ?

A . f_{1} (x) = \frac{\sin x}{3^{x} + 3^{- x}} B . f_{2} (x) = \frac{\cos x}{3^{x} + 3^{- x}}

C . f_{3} (x) = \log_{10} (x + \sqrt{x^{2} + 1})

D . f_{4} (x) = \frac{x^{2}}{10^{x} - 1}

Answered by Rasheed.Sindhi last updated on 08/Feb/22

B . f_{2} (- x) = \frac{\cos (- x)}{3^{- x} + 3^{- (- x)}} = \frac{\cos x}{3^{x} + 3^{- x}} = f_{2} (x)

∴ f_{2} i s a n e v e n f u n c t i o n .