f(x) = x^4+x^3+x^2+x+1 .

To find f(1) and f(-1).

To get f(1) , we put x = 1 in inthe expression. and evaluete the expression.

f(x) = x^4+x^3+x^2+x+1. Put x = 1and we get:

f(1) = 1^4+1^3+1^2+1+1 = 5

So f(1) = 5.

To get f(-1) , we put x = -1 in f(x) = x^4+x^3+x^2+x+1 and we get:

f(-1) = (-1)^4+(-1)^3+(-1)^2+(-1)+1

f(-1) = 1 -1 +1 -1+1 = 3-2 = 1.

So f(-1) = 1.

f(-1)

Each time when we have to determine the value of a polynomial, for a specific value of x, we'll have to substitute x by the given value, in the expression of the polynomial.

To calculate the values of the function for x = 1 and x = -1, we'll have to substitute x by 1 and by 01 in the expression of the function.

f( 1 ) = 1^4 + 1^3 + 1^2 + 1 + 1

**f(1) = 5**

f(-1) = ( -1 )^4 + ( - 1 )^3 + (-1 )^2 + ( - 1) + 1

f(-1) = 1 - 1+ 1 -1 + 1

We'll eliminate like terms:

**f(-1) = 1**