Question

True or False The exponential function $f\left(x\right)=e^x$ is increasing on the interval $(-\infty ,\infty )$. (p. 280)

Short answer

The statement is true

Step-by-step solution

Given information

Given function$f\left(x\right)=e^x$

Checking the domain

Checking, we get

By the properties of the exponential function $f\left(x\right)=a^x,a>1$, we know that its domain is the set of all real numbers $(-\infty ,\infty )$Also, it is an increasing function and is one-to one.

Therefore, the exponential function $f\left(x\right)=e^x$ is increasing on the interval $(-\infty ,\infty )$. The statement is true.