Let \( f:\mathbb{R}\to \mathbb{R} \) be a function defined byThen which of the following statements is TRUE?
\( f(x)=0 \) has infinitely many solutions in the interval \( \left[\dfrac{1}{10^{10}},\,\infty\right) \).
\( f(x)=0 \) has no solutions in the interval \( \left[\dfrac{1}{\pi},\,\infty\right) \).
The set of solutions of \( f(x)=0 \) in the interval \( \left(0,\,\dfrac{1}{10^{10}}\right) \) is finite.
\( f(x)=0 \) has more than \( 25 \) solutions in the interval \( \left(\dfrac{1}{\pi^{2}},\,\dfrac{1}{\pi}\right) \).
