How do you find the domain and range of #2 / x^2#?

1 Answer
Aug 23, 2017

Answer:

Domain: #{x| x≠0}#
Range: #{y| y>0}#

Explanation:

The domain is the input of the function. In this case, the domain has a restriction. The denominator can never be equal to 0. Since we have #x^2# in the denominator, we must set that equal to 0 to find what values of x are not allowed.

#x^2≠0 ->#

#sqrt(x^2)≠sqrt(0)#

#x≠0#

Our domain is #{x|x≠0}#.

Next is to find the range. In this case, note that the range cannot be equal to 0 since we have a variable in the denominator. To find the range, you can plug in numbers to find out what the range is. There is a simpler way to find it. If you input smaller numbers for x, your output for y will be larger. A larger input for x will result in a smaller input for y. As seen in the following graph, the range approaches but never touches or crosses the x-axis. The range also goes to infinity, so the the range is #{y|y>0}#.

graph{2/(x^2) [-10, 10, -5, 5]}