Chapter 4, Problem 120CR

To determine

To graph: the function and its reciprocal function.

Explanation of Solution

Given information:

Need to create graph function $f\left(x\right)=-2\sec \left(4x+\pi \right)$ .

Also create graph of reciprocal function of $f\left(x\right)$ .

Graph:

Give function is $f\left(x\right)=-2\sec \left(4x+\pi \right)$ .

Reciprocal function of $f\left(x\right)$ say $r\left(x\right)=-2\cos \left(4x+\pi \right)$ .

Graph of $f\left(x\right)=-2\sec \left(4x+\pi \right)$ is represented by red curve and Graph of reciprocal function $r\left(x\right)=-2\cos \left(4x+\pi \right)$ is represented by blue curve.

  

Interpretation:

Range of $f\left(x\right)$ is $\left(-\infty ,-2\right]\cup \left[2,\infty \right)$ and Range of reciprocal function $r\left(x\right)$ is $\left[-2,2\right]$ .

Domain of $f\left(x\right)$ is $x\in R,x\ne \frac{n\pi }{8}$ and Domain of reciprocal function $r\left(x\right)$ is $x\in R.$

Period of both the function is $\pi$ .

On comparing the graph of $f\left(x\right)=-2\sec \left(4x+\pi \right)$ and its reciprocal function, it can be said that when $f\left(x\right)$ is minimum , its reciprocal have maximum value and graph of $f\left(x\right)$ is not defined at the points when its reciprocal function’s value is zero.