Question

The exponential function $f\left(x\right)=e^x$ is a continuous function with domain $R$ and range

• A. $[-\infty ,\infty ]$
• B. $(-\infty ,\infty )$
• C. $(0,\infty )$
• D. $[0,\infty ]$

Answer 1

The correct option is C $(0,\infty )$

$y=e^x$. The domain is the set of all real numbers. Now taking log on both sides, we get
$lny=x$. Now logarithm function is only valid for all real numbers greater than 0. Thus the values of 'y' include all real numbers greater than 0.
Hence range of $f\left(x\right)$ is $R^{+}$ or $(0,\infty )$.