Let f(x) = (ax + b)/(x + 1), if limx → 0 f(x) = 2 and limx → ∞ f(x) = 1, then show that f(-2) = 0

Question

Let f(x) = \(\frac{ax+b}{x+1}\), if \(\lim\limits_{x \to 0}f(x)\) = 2 and \(\lim\limits_{x \to \infty}f(x)\) = 1, then show that f(-2) = 0

Answer 1

Given that \(\lim\limits_{x \to 0}f(x)\) = 2

b = 2

Also given that \(\lim\limits_{x \to \infty}f(x)\) = 1

Hence Proved.