Question

Given the function f(x) = 2x + 6/x^2 + 5x + 6 , evaluate the function with the domain values {-3, -2, 0, 2, 3}. What is the valid domain of this function? Show all work.

Answer 1

domain; x<0 or x>0

Explanation:

We have been given the following function;

f(x) = 2x + 6/x^2 + 5x + 6

We need to evaluate the values of f(x) for the following domain values;

{-3, -2, 0, 2, 3}

f(-3) = 2(-3) + 6/(-3)^2 + 5(-3) + 6

= -43/3

f(-2) = 2(-2) + 6/(-2)^2 + 5(-2) + 6

= -6.5

f(0) = 2(0) + 6/(0)^2 + 5(0) + 6

= undefined

f(2) = 2(2) + 6/(2)^2 + 5(2) + 6

= 21.5

f(3) = 2(3) + 6/(3)^2 + 5(3) + 6

= 83/3

The function is real and defined for every value of x in its domain except where x = 0 . This is a point of discontinuity.

Find the attachment below;