Let S1: If a function is not monotonic, then it does not have an inverse function.S2: If a function is not monotonic on (a,b), then its square cannot be monotonic on (a,b).S3: If both functions f(x) and g(x) are continuous and monotonic on ℝ, then their sum f(x)+g(x) is also monotonic or constant on ℝ.The number of statements among the S1,S2,S3 which are always true for every function

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Let $S_{1} :$ If a function is not monotonic, then it does not have an inverse function.
$S_{2} :$ If a function is not monotonic on $(a, b),$ then its square cannot be monotonic on $(a, b) .$
$S_{3} :$ If both functions $f (x)$ and $g (x)$ are continuous and monotonic on $ℝ$ , then their sum $f (x) + g (x)$ is also monotonic or constant on $ℝ .$
The number of statements among the $S_{1}, S_{2}, S_{3}$ which are always true for every function