Draw the graph of the function: Solve `|(x^2)/(x-1)|lt=1` using the graphical method.

Explanation

We have `|(x^(2))/(x-1)|`
or `" "x^(2) le |x-1|, x ne 1" "`(i)
To solve the inequality, we draw the graphs of `y=x^(2) and y= |x-1|` as shown in the adjacent figure.
Solving `y= |x-1| and y=x ^(2)` for their points of intersection A and B, we have `x-1=x^(2) or x^(2)-x-1=0`
or `" "x= (-1 pm sqrt5)/(2)`
The solution set of (i) is the set of those values of x for which the graph of `y= x^(2)` lies below the graph of `y=x-1`
From the graph, the solution is `[(-1-sqrt5)/(2), (-1+sqrt5)/(2)]`