Define q(x)= cases x-1 x-2 , & -1 x<2, 3-x, & 2 x 4

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Define

q(x)=\begin{cases} \dfrac{x-1}{x-2}, & -1\le x<2,\\ 3-x, & 2\le x\le 4. \end{cases}

Explain briefly why the fact that

q(-1)

and

q(4)

have opposite signs does not, by itself, guarantee that the equation

q(x)=0

has a solution on

[-1,4]