if-f-x-f-x-1-x-find-f-x-

Question Number 82570 by jagoll last updated on 22/Feb/20

i f f (x) = f (x + 1) - x

f i n d f (x)

Commented by Tony Lin last updated on 22/Feb/20

f (x + 1) - f (x) = x

\Rightarrow f (0) = f (1)

\Rightarrow f (x) = k x (x - 1) + c

k [(x + 1) x - x (x - 1)] = x

k = \frac{1}{2}

\Rightarrow f (x) = \frac{1}{2} x (x - 1) + c