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Mathematics
Mathematics
Problem
For
m
∈
R
m\in\mathbb R
m
∈
R
, define
h
m
(
x
)
=
x
2
+
2
(
m
−
1
)
x
+
m
2
−
4
m
+
3
h_m(x)=x^{2}+2(m-1)x+m^{2}-4m+3
h
m
(
x
)
=
x
2
+
2
(
m
−
1
)
x
+
m
2
−
4
m
+
3
. a. (i) Find the minimum value of
h
m
h_m
h
m
in terms of
m
m
m
. b. (ii) Hence, find all real values of
m
m
m
for which the range of
h
m
h_m
h
m
is
[
2
,
∞
)
[2,\infty)
[
2
,
∞
)
.
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