Name: The Silent Wind of Doom 2008-12-14 19:29
Show me what ya got.
1) If f(x) + f\left(\frac{1}{1-x}\right) = x+1 for all x \ne 1, find a formula for f(x).
2) If a,b,c,d are distinct
numbers such that for some number k
a^4+a^2+ka+64=0
b^4+b^2+kb+64=0
c^4+c^2+kc+64=0
d^4+d^2+kd+64=0
find a^2 + b^2 + c^2 + d^2.
3) Let f be an infinitely differentiable function on [0,1). Extend f to \mathbb{R^+} by defining f(x) = f(x-1) + f'(x-1) when x \ge 1. Find a one term expression for f involving only elementary functions, the differentiation operator, the floor operator, and f evaluated on [0,1).
(inb4 the TeX's all fucked up)
1) If f(x) + f\left(\frac{1}{1-x}\right) = x+1 for all x \ne 1, find a formula for f(x).
2) If a,b,c,d are distinct
numbers such that for some number k
a^4+a^2+ka+64=0
b^4+b^2+kb+64=0
c^4+c^2+kc+64=0
d^4+d^2+kd+64=0
find a^2 + b^2 + c^2 + d^2.
3) Let f be an infinitely differentiable function on [0,1). Extend f to \mathbb{R^+} by defining f(x) = f(x-1) + f'(x-1) when x \ge 1. Find a one term expression for f involving only elementary functions, the differentiation operator, the floor operator, and f evaluated on [0,1).
(inb4 the TeX's all fucked up)