Question

The function f (x) = log(x + √(x² + 1)) is
(a) an odd function
(b) a periodic function
(c) neither an even nor an odd function
(d) an even function.

Answer 1

(a) f(x) = log[√(x² + 1) +x]

Therefore, f(-x) = log[√(1+x²) -x]

= -log[1/√(1+x²)-x] = -log[√(1+ x² )+ x)/1]

= - f(x) => f(x) + f(-x) = 0

=> f(x) is an odd function.