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Problems
Define
q
(
x
)
=
{
x
−
1
x
−
2
,
−
1
≤
x
<
2
,
3
−
x
,
2
≤
x
≤
4.
q(x)=\begin{cases} \dfrac{x-1}{x-2}, & -1\le x<2,\\ 3-x, & 2\le x\le 4. \end{cases}
q
(
x
)
=
⎩
⎨
⎧
x
−
2
x
−
1
,
3
−
x
,
−
1
≤
x
<
2
,
2
≤
x
≤
4.
…
Mathematics
Problem
Define
q
(
x
)
=
{
x
−
1
x
−
2
,
−
1
≤
x
<
2
,
3
−
x
,
2
≤
x
≤
4.
q(x)=\begin{cases} \dfrac{x-1}{x-2}, & -1\le x<2,\\ 3-x, & 2\le x\le 4. \end{cases}
q
(
x
)
=
⎩
⎨
⎧
x
−
2
x
−
1
,
3
−
x
,
−
1
≤
x
<
2
,
2
≤
x
≤
4.
Explain briefly why the fact that
q
(
−
1
)
q(-1)
q
(
−
1
)
and
q
(
4
)
q(4)
q
(
4
)
have opposite signs does not, by itself, guarantee that the equation
q
(
x
)
=
0
q(x)=0
q
(
x
)
=
0
has a solution on
[
−
1
,
4
]
[-1,4]
[
−
1
,
4
]
.
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