Thread: Set of values of X

Sketch the graph of , where . Hence find the set of values of x such that

Originally Posted by Punch

Sketch the graph of y=\frac{(2(x+a))}{(x-1)}, where . Hence find the set of values of x such that \frac{2(x+a)}{x-1}≤|x+a|

And what did your graph tell you?

-Dan

Originally Posted by topsquark

And what did your graph tell you?

-Dan

From my understanding, the 2 graphs would intersect at 2 points, but i doubt this could help in anyway. Is there something I overlooked?

Originally Posted by Punch

From my understanding, the 2 graphs would intersect at 2 points, but i doubt this could help in anyway. Is there something I overlooked?

Originally Posted by Punch

Sketch the graph of , where . Hence find the set of values of x such that

They intersect twice. Good. Now look at the inequality again. You are looking for all points on the 2(x + a)/(x - 1) curve that are lower on the graph (or equal to) the graph of |x + a|. So what parts of the function 2(x + a)/(x - 1) are below the lines?

-Dan

Originally Posted by topsquark

They intersect twice. Good. Now look at the inequality again. You are looking for all points on the 2(x + a)/(x - 1) curve that are lower on the graph (or equal to) the graph of |x + a|. So what parts of the function 2(x + a)/(x - 1) are below the lines?

-Dan

but i cant find out since i cant draw the graph of |x+a| without knowing the value of a