Let f:[−1,1]→[0,2] be a function defined by f(x)=mx+c where m>0. I – InterviewSolution

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1.	Let f:[−1,1]→[0,2] be a function defined by f(x)=mx+c where m>0. If f is onto and tan(tan−117+cot−18+cot−118) equals f(a) for some a∈[−1,1], then the value of [a]+9 is ([.] denotes the greatest integer function)
Answer» Let $f : [- 1, 1] \to [0, 2]$ be a function defined by $f (x) = m x + c$ where $m > 0.$ If $f$ is onto and $tan ({tan}^{- 1} \frac{1}{7} + {cot}^{- 1} 8 + {cot}^{- 1} 18)$ equals $f (a)$ for some $a \in [- 1, 1],$ then the value of $[a] + 9$ is ( $[.]$ denotes the greatest integer function)

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