(1)find the no. of solution of

f(x) = f ^-1(x)

if f(x) = x+(sin pi x) / pi.       where x belongs to (-3,25/3]

ans=

(a) 13(b) 14(c) 15(d) 16

plz explain me fully,...........

if a is the root of the eqn. f(x)=f^--1(x)....then f(x) =x @ x=a....

so we have x + sin (pix) /pi= x...(actually im not being able to make out wat uve written clearly)

or sin(pix)/pi =0....and using this u can get to the soln....but the main funda is as explained in the first line...

jus. given the brief method...

rate if useful...

First find f^-1(x).

Now, f(x) and f^-1(x)  are always symmetrical about  the line y = x.

So,  the intersection point of these two curves, will lie on the line y = x.

Hence, find the intersection of any of these curves with y=x. And that will be the solution.