Chapter 8, Problem 15SGR

To determine

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

Answer to Problem 15SGR

The domain is $x>R$ and the range is $R=\left\{f\left(x\right)\right\}f\left(x\right)>-1$.

Explanation of Solution

Given:

The given function is $f\left(x\right)=3{\left(\frac{1}{4}\right)}^{x+3}-1$ .

Calculation:

Consider the given function is,

  $f\left(x\right)=3{\left(\frac{1}{4}\right)}^{x+3}-1$

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 greater than $-1$ .

Thus, the domain is $x>R$ and the range is $R=\left\{f\left(x\right)\right\}f\left(x\right)>-1$.