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Mathematics
Problem
Define the piece-wise function
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
by
f
(
x
)
=
{
x
+
2
,
x
≤
1
,
a
x
+
b
,
x
>
1
,
f(x)=\begin{cases}x+2,& x\le 1,\\ ax+b,& x>1,\end{cases}
f
(
x
)
=
{
x
+
2
,
a
x
+
b
,
x
≤
1
,
x
>
1
,
where
a
a
a
and
b
b
b
are real constants. Which one of the following ordered pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
makes
f
f
f
bijective on
R
\mathbb R
R
? a)
(
2
,
5
)
(2,5)
(
2
,
5
)
b)
(
2
,
1
)
(2,1)
(
2
,
1
)
c)
(
−
1
,
4
)
(-1,4)
(
−
1
,
4
)
d)
(
0
,
3
)
(0,3)
(
0
,
3
)
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