Define f(x+y) = f(x) + f(y) - 1 for all real x and y such that f(x) is differentiable for all values of x with f ’(0) = cos A.

Determine whether or not the value of f(1) – cos A is equal to 2.

A was not defined, so I assume A is a constant

f(x) = cos(A)*x + 1
f(x+y) = cos(A)*(x+y) + 1
          = [cos(A)*x + 1] + [cos(A)*y + 1] - 1
f'(x) = cos(A) for all x,  so f'(0) = cos(A)

f(1) = cos(A) + 1   so  f(1) - cos(A) = 1    (not 2)

Posted by Larry on 2007-01-19 22:53:11