Question

Let $f:R\to R$ be a function defined by $f\left(x\right)=\{\begin{array}{cc}{x}^2+2mx-1,& x\le 0\\ mx-1,& x>0\end{array}.$ If $f$ is one-one, then $m$ can be

• A. $-5$
• B. $5$
• C. $4$
• D. $-4$

Answer 1

Answer: (A), (D)

The correct options are
A $-5$
D $-4$

For $f$ to be one-one, vertex of $y=x^2+2mx-1$ should lie to right of or on $y-$axis.


$\Rightarrow \frac{-2m}{2}\ge 0\Rightarrow m\le 0\cdots \left(1\right)$

And for line $y=mx–1$
$m<0\cdots \left(2\right)$
From $\left(1\right)$ and $\left(2\right)$, $m<0$