A) injective only
B) both injective as well as surjective
C) not injective but it is surjective
D) neither injective nor surjective
E) None of these
Correct Answer: E
Solution :
Here, \[f(x)=\left| 1-\frac{1}{x} \right|=\left| \frac{x-1}{x} \right|\]\[=\left\{ \begin{align} & \frac{1-x}{x},\,\,\,\,\,0<x<1 \\ & \frac{x-1}{x}\,\,\,\,\,\,\,x\ge 1 \\ \end{align} \right.\] \[\therefore \]f(x) is not injective but range of function is\[[0,\infty )\] Note: If co-domain is \[[0,\infty )\], then f(x) will be surjective.You need to login to perform this action.
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