Suppose that $f(x)$ is a function such that
\[f(xy) + x = xf(y) + f(x)\]for all real numbers $x$ and $y.$  If $f(-1) = 5$ then compute $f(-1001).$
Question:
Suppose that $f(x)$ is a function such that
\[f(xy) + x = xf(y) + f(x)\]for all real numbers $x$ and $y.$  If $f(-1) = 5$ then compute $f(-1001).$
Answer:
Let's think step by step.

user
2005
Suppose that $f(x)$ is a function such that
\[f(xy) + x = xf(y) + f(x)\]for all real numbers $x$ and $y.$  If $f(-1) = 5$ then compute $f(-1001).$
train