SOLUTION: Given that function f : x maps to 2/ax + b , such that f(0) = -2 and f(2) = 2, Find the values of a and of b, find the values of x for which f(x) = x , Show that f(p) + f(-p) = 2f(

Algebra ->  Test -> SOLUTION: Given that function f : x maps to 2/ax + b , such that f(0) = -2 and f(2) = 2, Find the values of a and of b, find the values of x for which f(x) = x , Show that f(p) + f(-p) = 2f(      Log On


   

Question 1182951: Given that function f : x maps to 2/ax + b , such that f(0) = -2 and f(2) = 2, Find the values of a and of b, find the values of x for which f(x) = x , Show that f(p) + f(-p) = 2f(p^2)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Will assume that f%28x%29+=+2%2F%28ax%2Bb%29
f(0) = -2 ==> f(0) = 2/b = -2 ==> b = -1 ==> f%28x%29+=+2%2F%28ax-1%29
f(2) = 2 ==> 2/(2a - 1) = 2 ==> a = 1 ==> f%28x%29+=+2%2F%28x-1%29
f(x) = x ==> 2%2F%28x-1%29+=+x ==> 2 = x(x-1) ==> x%5E2-x-2=0
<==> (x-2)(x+1) = 0 ==> x = 2 or -1.
Finally, .