Question

Suppose that $f(x)$ and $g(x)$ are functions on $\mathbb{r}$ such that the range of $f$ is $[-5,3]$, and the range of $g$ is $[-2,1]$. the range of $f(x) \cdot g(x)$ is $[a,b]$. what is the largest possible value of $b$

Answer 1

The largest possible value of b is 10, since for some x = x₀ it could be the case that f(x₀) = -5 and g(x₀) = -2; then f(x₀) g(x₀) = -5 × -2 = 10.