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Question Number 192286 by pete last updated on 14/May/23

$$\mathrm{Determine}\mathrm{whether}\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\mathrm{x}}({2\mathrm{x}}^2+1)\mathrm{is}:$$$$1.\mathrm{A}\mathrm{function}$$$$2.\mathrm{injective}$$$$3.\mathrm{surjective}$$$$4.\mathrm{bijective}$$

Answered by mehdee42 last updated on 14/May/23

$$ify=1\Rightarrow 2x^2-x+1=0\Rightarrow x=\frac{1\pm \sqrt{-3}}{4}\notin \mathbb{R}\Rightarrow fisnotsurjective$$$$f\left(a\right)=f\left(b\right)\Rightarrow (a-b)(2ab-1)=0\Rightarrow a=b\vee a=\frac{1}{2b}\Rightarrow fisnotinjective$$$$$$

Commented by mehdee42 last updated on 14/May/23

Commented by pete last updated on 14/May/23

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

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