Derivative with trigonometry

Calculus Level 3

Let f ( x ) = sin ⁡ x − cos ⁡ x + ln ⁡ x f(x)=\sin x - \cos x + \ln x .

How many roots of f ( x ) f(x) are there on the domain ( 0 , ∞ ) (0,\infty) ?

Note: Without using a graph software and give a rigorous proof.

0 2 Infinite many 1 3

Alice Smith by Alice Smith , 20, China

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