f:(1,3)→R is a function defined by f(x)=x[x]x2+1. Let the range of f – InterviewSolution

1.	f:(1,3)→R is a function defined by f(x)=x[x]x2+1. Let the range of f be (a1,a2)∪(b1,b2]. If fundamental period of cot(a1a2b1b2x+32) is pπq, where gcd(p,q)=1, then the value of p+q is
Answer» $f : (1, 3) \to R$ is a function defined by $f (x) = \frac{x [x]}{x^{2} + 1} .$ Let the range of $f$ be $(a_{1}, a_{2}) \cup (b_{1}, b_{2}] .$ If fundamental period of $cot (\frac{a_{1} a_{2}}{b_{1} b_{2}} x + \frac{3}{2})$ is $\frac{p π}{q},$ where $gcd (p, q) = 1,$ then the value of $p + q$ is

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