Chapter 11.3, Problem 4CFU

To determine

To find: the domain and range of the function $f\left(x\right)=e^x$ .

Answer to Problem 4CFU

  $D=\left\{x:x\in R\right\}$ and $R=\left\{y:y\in w\right\}.$

Explanation of Solution

Given:

  $f\left(x\right)=e^x$ .

Concept used:

The value of $e\sim 2.7$ which implies the range is ${\left(2.7\right)}^x$ which is always greater than zero.

The domain is $x$ and range is $f\left(x\right)$ or $y$ .

Calculation:

According to the given the function is:

  $f\left(x\right)=e^x$ .

Domain: the exponential is defined for all real numbers.

  $D=\left\{x:x\in R\right\}$ .

Range:

  $e^x$ is always positive, its values range from $0$ to infinity.

The value of $e\sim 2.7$ which implies the range is ${\left(2.7\right)}^x$ .

By putting real numbers range will be all positive real number.

  $R=\left\{y:y\in w\right\}.$

Here $R$ is range and $w$ is the whole number.

Hence, the $D=\left\{x:x\in R\right\}$ and $R=\left\{y:y\in w\right\}.$