0 votes 0 votes Let $f(x) = \dfrac{2x}{x-1}, \: x \neq 1$. State which of the following statements is true. For all real $y$, there exists $x$ such that $f(x)=y$ For all real $y \neq 1$, there exists $x$ such that $f(x)=y$ For all real $y \neq 2$, there exists $x$ such that $f(x)=y$ None of the above is true Calculus isi2014-dcg calculus functions + – Arjun asked Sep 23, 2019 • recategorized Nov 9, 2019 by Lakshman Bhaiya Arjun 424 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes $f(x)=\frac{2x}{x-1}=y $ $\Rightarrow 2x=yx-1 $ $\Rightarrow x=\frac{1}{y-2}$ Thus $y\neq2$ for x to exist. Hence Option(C) for all real $y\neq2$, there exists $x$ such that $f(x)=y$ Sourajit25 answered Sep 24, 2019 Sourajit25 comment Share Follow See all 0 reply Please log in or register to add a comment.