Another (same) Numerical Analysis Question...?

[javaHungerForce]

Find a linear tranformation of x=x(u) that will take the interval 0<=u<=1 onto the interval -1<=x<=1.

And how do you find the inverse tranformation u=u(x) that takes the interval -1<=x<=1 onto the interval 0<=u<=1

SHOW HOW THIS IS DONE.

[gp4rts]

He linear transformation will be of the form x(u) = a*u+b; when u = 0, x is -1, this means b = -1; when u = 1, x = 1 so 1 = a - 1, or a = 2. The transformation is then x(u) = 2*u-1

u(x) = a*x+b; when x=-1, u = 0 -a + b = 0, a = b; u(x) = ax+a. when x=1, u = 1, a+a=1 a = .5

u(x) = .5*x+.5