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Mathematics
Mathematics
Problem
Let
f
:
[
−
1
,
4
]
→
R
f:[-1,4]\rightarrow \mathbb R
f
:
[
−
1
,
4
]
→
R
be given by
f
(
x
)
=
x
2
f(x)=x^2
f
(
x
)
=
x
2
and
g
:
(
−
∞
,
2
]
→
R
g:(-\infty,2]\rightarrow \mathbb R
g
:
(
−
∞
,
2
]
→
R
be given by
g
(
x
)
=
3
x
−
7
g(x)=3x-7
g
(
x
)
=
3
x
−
7
. A new function
h
h
h
is defined wherever both
f
f
f
and
g
g
g
are defined by
h
(
x
)
=
f
(
x
)
+
g
(
x
)
h(x)=f(x)+g(x)
h
(
x
)
=
f
(
x
)
+
g
(
x
)
. a. (i) Determine the domain of
h
h
h
.},{ b. (ii) Find the range of
h
h
h
over this domain.
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