Mathematics - Functions Question with Solution | TestHub

On each of the intervals $(1,2)$ and $(2,3),f$ is continuous and takes all real values (from $+\infty$ to $-\infty$ ), so every real value is attained at least twice; $f$ is many-one and statement 1 is true. Also $f^{\prime }(x)=-\frac{1}{(x-1{)}^2}-\frac{2}{(x-2{)}^2}-\frac{3}{(x-3{)}^2}<0$ for every $x$ in the domain of $f$, but the function is not one-one (the domain is disconnected), so statement 2 is false. \end{document}