Chapter 6.1, Problem 2CE

a.

To determine

Find the value of given algebraic function.

Answer to Problem 2CE

At the different value of $x=2,13,22,50,99$ , the solution of the algebraic functions is

  $\left[\text{3 14 23 51 100}\right]$

Explanation of Solution

Given: The function is given

  $f(x)=\frac{x^5+1}{x^4-x^3+x^2-x+1}$

And the value of x is also given

  $x=2,13,22,50,99$

Calculation:

Let’s take all the values of x, put into the given algebraic function and find the solution.

Here we have used MATLAB to simplify the function.

program:

clc
clear
close all
symsx
f=(x^5+1)./(x^4-x^3+x^2-x+1);
a=[2,13,22,50,99];
fori=1:5
    I=subs(f,x,a(i));
ans(i)=double(I);
end

Query:

• First, we have defined the given function.
• Then define the value of x.
• The using function “subs” in MATLAB to put the values of x into the function and get the solution.

b.

To determine

Explain the solution of the algebraic function

Answer to Problem 2CE

The solution is

  $f(x=2)=3$

Explanation of Solution

Given: The functions are given

  $f(x)=\frac{x^5+1}{x^4-x^3+x^2-x+1}$

And the value of x is also given

  $x=2,13,22,50,99$

Calculation:

Let’s take $x=2$

We know that the function is

  $f(x)=\frac{x^5+1}{x^4-x^3+x^2-x+1}$

Put the value of x=2

  $\begin{array}{l}f(x=2)=\frac{2^5+1}{2^4-2^3+2^2-2+1}\\ f(x=2)=\frac{32+1}{16-8+4-2+1}\\ f(x=2)=\frac{33}{21-10}\\ f(x=2)=3\end{array}$