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Mathematics
Problem
Let
f
(
x
)
=
x
2
−
1
x
+
2
f(x)=\dfrac{x^{2}-1}{x+2}
f
(
x
)
=
x
+
2
x
2
−
1
and
g
(
x
)
=
x
−
1
x
−
2
g(x)=\dfrac{x-1}{x-2}
g
(
x
)
=
x
−
2
x
−
1
. a. (i) Find
(
f
g
)
(
x
)
\left(\dfrac{f}{g}\right)(x)
(
g
f
)
(
x
)
and simplify your answer. b. (ii) State the domain of the simplified function.
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