Chapter 8, Problem 16SGR

To determine

To find: The domain and the range of the given equation.

Answer to Problem 16SGR

The domain is $x>R$ and the range is $R=\left\{f\left(x\right)\right\}f\left(x\right)>0$.

Explanation of Solution

Given:

The given function is $f\left(x\right)=\frac{3}{5}{\left(\frac{2}{3}\right)}^{x-2}+3$ .

Calculation:

Consider the given function is,

  $f\left(x\right)=\frac{3}{5}{\left(\frac{2}{3}\right)}^{x-2}+3$

The graph for the above function is shown in Figure 1

  

Figure 1

The graph shows the domain is all the real numbers and the range is all the positive real numbers.

Thus, the domain is $x>R$ and the range is $R=\left\{f\left(x\right)\right\}f\left(x\right)>0$.