Chapter 1.6, Problem 112E

a.

To determine

To graph: the function $f(x)=\frac{1}{x^3+x^2+x+1}$

Explanation of Solution

Given: $f(x)=\frac{1}{x^3+x^2+x+1}$

Graph:

  

b.

To determine

To graph: the inverse relation of function $f(x)=\frac{1}{x^3+x^2+x+1}$

Explanation of Solution

Given: $f(x)=\frac{1}{x^3+x^2+x+1}$

Graph:

  

c.

To determine

To find: whether the inverse relation is an inverse function or not.

Answer to Problem 112E

The inverse relation is a function.

Explanation of Solution

Given: $f(x)=\frac{1}{x^3+x^2+x+1}$ and graph of inverse relation as

  

Concept used:

For a relation f(x) to be a function graph of f(x) should not have any vertical line which crosses it twice, i.e. if any vertical line cuts the graph at two or more points then the relation is not a function.

As there does not exist any vertical line which crosses the graph twice, given function is a relation.