Practicing Success
The function f : R – {–1} → R – {1} defined by $f(x) = \frac{x}{x+1}$ is |
Both 1-1 and onto Only 1-1 Only onto Neither 1-1 nor onto |
Both 1-1 and onto |
f : R – {–1} → R – {1} $f(x) = \frac{x}{x+1} =y$ so $y_1 = y_2 ⇒ \frac{x_1}{x_1+1} = \frac{x_2}{x_2+1}$ $\Rightarrow x_1\left(x_2+1\right)=x_2\left(x_1+1\right)$ $\Rightarrow x_2 x_1+x_1=x_2 x_1+x_2$ $\Rightarrow x_1=x_2$ ⇒ function is one one. so $y=\frac{x}{x+1} \Rightarrow xy + y = x \Rightarrow y = x(1-y)$ so $x = \frac{y}{1-y}$ → for every y atleast some x exist ⇒ it is onto Option A |