Chapter 8, Problem 13SGR

To determine

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

Answer to Problem 13SGR

The domain of consists of all the real numbers and the range consists is $R=\left\{f\left(x\right)\right\}f\left(x\right)>-6$ .

Explanation of Solution

Given:

The given function is $f\left(x\right)=3{\left(4\right)}^x-6$ .

Calculation:

Consider the given function is,

  $f\left(x\right)=3{\left(4\right)}^x-6$

The graph for the above function is shown in Figure 1

  

Figure 1

The graph shows that the domain consists of all the real numbers and the range has all the real numbers that are less than $-6$ .

Thus, the domain of consists of all the real numbers and the range consists is $R=\left\{f\left(x\right)\right\}f\left(x\right)>-6$ .