Question Number 122998 by benjo_mathlover last updated on 21/Nov/20
![f:R→R f(x) = { ((x^2 +2mx−1 ; x≤0)),((mx−1 ; x>0)) :} if f(x) is one−one then m lies in interval (a) (−∞,0 ) (c) (0,∞) (b) (−∞, 0 ] (d) [ 0, ∞ )](https://www.tinkutara.com/question/Q122998.png)
$$\:{f}:{R}\rightarrow{R}\: \\ $$$$\:{f}\left({x}\right)\:=\:\begin{cases}{{x}^{\mathrm{2}} +\mathrm{2}{mx}−\mathrm{1}\:;\:{x}\leqslant\mathrm{0}}\\{{mx}−\mathrm{1}\:;\:{x}>\mathrm{0}}\end{cases} \\ $$$${if}\:{f}\left({x}\right)\:{is}\:{one}−{one}\:{then}\:{m}\:{lies}\: \\ $$$${in}\:{interval}\: \\ $$$$\left({a}\right)\:\left(−\infty,\mathrm{0}\:\right)\:\:\:\:\:\left({c}\right)\:\left(\mathrm{0},\infty\right) \\ $$$$\left({b}\right)\:\left(−\infty,\:\mathrm{0}\:\right]\:\:\:\:\:\left({d}\right)\:\left[\:\mathrm{0},\:\infty\:\right)\: \\ $$