Chapter 1.3, Problem 45E

To determine

Tofind:The correct option for the range of the function $f\left(x\right)=4-2^{2x}$ .

Answer to Problem 45E

The correct option is (B) as the range of the function $f\left(x\right)=4-2^{2x}$ is the interval $\left(-\infty ,4\right)$ .

Explanation of Solution

Given information:The function is $f\left(x\right)=4-2^{2x}$ .

Calculation:

The range a function of the form $-c\cdot n^{ax+b}+k$ is $f\left(x\right)<k$ . Consider the given function.

  $\begin{array}{c}f\left(x\right)=4-2^{2x}\\ =-2^{2x}+4\end{array}$

For the given function $f\left(x\right)<4$ . So, the range is the set of all values less than 4 that is the interval $\left(-\infty ,4\right)$ .

Therefore, the correct option is (B) as the range of the function $f\left(x\right)=4-2^{2x}$ is the interval $\left(-\infty ,4\right)$ .