The interval of monotonicity of the function \( f(x)=\frac{x}{\log _{\theta} x} \), is (a) incre...

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The interval of monotonicity of the function \( f(x)=\frac{x}{\log _{\theta} x} \), is
(a) increases when \( x \in(e, \infty) \) and decreases when \( x \in(0, \theta) \)
(b) increases when \( x \in(\theta, \infty) \) and decreases when \( x \in(0, \theta)-\{1\} \)
(c) increases when \( x \in(0, \theta) \) and decreases when \( x \in(\theta, \infty) \)
(d) increases when \( x \in(0, \theta)-\{1\} \) and decreases when \( x \in(\theta, \infty) \)
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