Question

The amplitude of a wave disturbance propagating in the positive x-direction is given by y = 1/(1 + x2 ) at time t = 0 and y = 1/[1 + (x – 1)2 ] at t = 2 seconds where x and y are in metres. the shape of the wave disturbance does not change during the propagation. the velocity of the wave is

Answer 1

here,
   y = 1/(1 + x²)            at     t = 0 sec
   y = 1/[ 1 + (x - 1)²]   at     t = 2 sec

according to mathematics,[play with graph], if f(x) = f(x-1), it means shape of graph is same just change the position. graph shift right direction by 1 unit.
Here it is clear that the shape of wave doesn't change. also wave move in 2 sec , 1m in positive x direction.
  so, wave moves 1 m in 2 sec .
so, velocity of wave = displacement of wave / time taken
                                  = 1m/2sec = 0.5 m/sec 
hence, velocity of wave = 0.5 m/s 

Answer 2

here is your answer bro ....