f(x) = 9 – x^2, g(x) = 3 – x. Find (f – g)(x) and its domain.
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Answer:
f
(
x
)
=
x
2
−
9
,
g
(
x
)
=
3
−
x
Set up the composite result function.
f
(
g
(
x
)
)
Evaluate
f
(
g
(
x
)
)
by substituting in the value of
g
into
f
.
f
(
3
−
x
)
=
(
3
−
x
)
2
−
9
Simplify each term.
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f
(
3
−
x
)
=
9
−
6
x
+
x
2
−
9
Combine the opposite terms in
9
−
6
x
+
x
2
−
9
.
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