Hi, there--
THE PROBLEM:
What is the domain of the function h(x)=8x/(x(x^2-81))?
A SOLUTION:
In this case you want to restrict from the domain of all real numbers, those values that make the denominator equal 0. (Division by zero is not defined.)
We simply set the denominator equal to zero and solve for x.
The expression {x^2-81}}} is the difference of two squares, and factors as (x-9)(x+9)
Then x = 0 OR x - 9 = 0 OR x + 9 = 0
x = 0 OR x = 9 OR x = -9
Consequently, the domain of the function h is all real numbers except -9, 0, and 9.
In bracket notation, we have
(-infinity,-9) U (-9,0) U (0, 9) U (9, infinity)
Hope this helps! Feel free to email if you have any questions about the solution.
Good luck with your math,
Mrs. F
math.in.the.vortex@gmail.com
