Question

# Check the injectivity and surjectivity of the following functions:$$f: Z \rightarrow Z$$ given by $$f(x)=x^2$$

Solution

## $$f(x)=x^2$$It is seen that $$f(-1)=f(1)=1$$, but $$-1 \neq 1$$$$\therefore f$$ is not injective.Now, $$-2 \in Z$$. But, there does not exist anyelement $$x\in Z$$ such that $$f(x)=x^2=-2$$$$\therefore f$$ is not surjective.Hence, function $$f$$ is neither injective nor surjective.MathematicsRS AgarwalStandard XII

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