Question

The number of points of intersection of the graphs of the functions $y=f\left(x\right)$ and $y=\varphi \left(x\right)$ give the number of solutions of the equation $f\left(x\right)-\varphi \left(x\right)=0$. Let $f\left(x\right)=k{e}^x$ and $\varphi \left(x\right)=x$, where k is a real constant.

The line $y=x$ meets the curve $y=k{e}^x$ for $k\le 0$ at

• A. no point
• B. one point
• C. two points
• D. more than two points

Answer 1

The correct option is B one point

from the figure:
for: $k\le 0$
point of intersection of $y=x$ & $y=e^x$ is only one
Ans: B