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Mathematics
Mathematics
Problem
Consider the functions
f
,
g
:
R
→
R
f,g:\mathbb{R}\to \mathbb{R}
f
,
g
:
R
→
R
given by
f
(
x
)
=
2
x
+
3
,
g
(
x
)
=
1
x
−
5
f(x)=2x+3, \quad g(x)=\dfrac{1}{x-5}
f
(
x
)
=
2
x
+
3
,
g
(
x
)
=
x
−
5
1
(
x
≠
5
)
(x\neq5)
(
x
=
5
)
. (a) Find the expression for
(
g
∘
f
)
(
x
)
(g\circ f)(x)
(
g
∘
f
)
(
x
)
. (b) Determine the domain of
(
g
∘
f
)
(g\circ f)
(
g
∘
f
)
. (c) Find the expression for
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
together with its domain.
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