Find the number of solutions of the equation |1|x| -1| = x + sin(x)
23graphs can help...
graph of x+sinx will be like , graph of sinx on the line y=x
draw graph for 1/(x-1) , remove the graph for on LHS of y axis , and on LHS, draw mirror image of graph on RHS of y axis
then remove the graph below x axis ,and draw mirror image of graph above x axis , pt(s) of intersection of dis graph with x + sinx will be the solution(s)
1daw graph of x+sinx & draw graph for 1/(x-1) , draw mirror image of graph on RHS of y axis
then remove the graph below x axis ,and draw mirror image of graph above x axis , pt(s) of intersection of dis graph with x + sinx will be the solution(s)
21from the graphs i think if there is a solution it must be in the interval (1,2)
because if x> 2 ,1/(x-1) is <1 and x+ sin x is always greater than 1
if x is in (1,2) 1/(x-1) is > 1 and so is (x+ sin x)
