How do solve #1/x^2-1<=0# graphically?

1 Answer
Jan 9, 2018

Answer:

#x<=-1 or x>=1#

Explanation:

#1/x^2 - 1 <= 0#

First, add 1 to both sides so that you end up with #1/x^2# on the left, to make graphing a bit easier

#1/x^2 <= 1#

Then, plot the graph of #y=1/x^2#

graph{1/x^2 [-10, 10, -5, 5]}

To find the range of x for which #1/x^2 <= 1# is true, just find the range of x for which #y<=1# in the graph above

graph{(y-1/x^2)(y-1)=0 [-10, 10, -5, 5]}

As you can see from this graph, #1/x^2# drops below #y=1# when #x<=-1# and #x>=1#

Thus the solution to #1/x^2 <= 1#, and thus #1/x^2 -1 =0#, is #x<=-1 or x>=1#