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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, ∞ )

$$\:{f}:{R}\rightarrow{R}\: \\ $$ $$\:{f}\left({x}\right)\:=\:\begin{cases}{{x}^{\mathrm{2}} +\mathrm{2}{mx}−\mathrm{1}\:;\:{x}\leqslant\mathrm{0}}\\{{mx}−\mathrm{1}\:;\:{x}>\mathrm{0}}\end{cases} \\ $$ $${if}\:{f}\left({x}\right)\:{is}\:{one}−{one}\:{then}\:{m}\:{lies}\: \\ $$ $${in}\:{interval}\: \\ $$ $$\left({a}\right)\:\left(−\infty,\mathrm{0}\:\right)\:\:\:\:\:\left({c}\right)\:\left(\mathrm{0},\infty\right) \\ $$ $$\left({b}\right)\:\left(−\infty,\:\mathrm{0}\:\right]\:\:\:\:\:\left({d}\right)\:\left[\:\mathrm{0},\:\infty\:\right)\: \\ $$

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