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Mathematics
Mathematics
Problem
Consider the three functions on suitable subsets of
R
\mathbb{R}
R
:
f
(
x
)
=
∣
x
−
1
∣
,
g
(
x
)
=
1
x
+
2
,
h
(
x
)
=
x
2
−
9
.
f(x)=|x-1|,\; g(x)=\dfrac{1}{x+2},\; h(x)=\sqrt{x^{2}-9}.
f
(
x
)
=
∣
x
−
1∣
,
g
(
x
)
=
x
+
2
1
,
h
(
x
)
=
x
2
−
9
.
a. (i) Form the function
F
(
x
)
=
2
f
(
x
)
−
3
g
(
x
)
+
h
(
x
)
F(x)=2f(x)-3g(x)+h(x)
F
(
x
)
=
2
f
(
x
)
−
3
g
(
x
)
+
h
(
x
)
and simplify the expression as far as possible. b. (ii) Determine the domain of
F
(
x
)
F(x)
F
(
x
)
.
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