Question

Let f : (0, ∞) → R be given by f(x) =∫e ^{– (t + 1/t)}dt/t for t ∈ [1/x, x], then

(a) f(x) is monotonic inc. on [1, ∞).

(b) f(x) is monotonic dec. on (0, 1).

(c) f(x) + f (1/x) = 0, for all x ∈ (0, ∞).

(d) f(2^x) is an odd function of x on R.

Answer 1

Correct option (a, c, d)

Explanation:

Thus, f is monotonic increasing on [1, ∞)

Thus, g (x) is an odd function.

So, f(2^x) is an odd function.