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Mathematics
Problem
Define three functions
f
(
x
)
=
ln
(
x
2
+
1
)
f(x)=\ln\left(x^{2}+1\right)
f
(
x
)
=
ln
(
x
2
+
1
)
,
g
(
x
)
=
sin
x
g(x)=\sin x
g
(
x
)
=
sin
x
and
h
(
x
)
=
e
x
h(x)=e^{x}
h
(
x
)
=
e
x
. (i) Obtain a simplified expression for
(
h
∘
g
∘
f
)
(
x
)
(h\circ g\circ f)(x)
(
h
∘
g
∘
f
)
(
x
)
. (ii) Determine the domain of
(
h
∘
g
∘
f
)
(h\circ g\circ f)
(
h
∘
g
∘
f
)
. (iii) Evaluate
(
h
∘
g
∘
f
)
(
1
)
(h\circ g\circ f)(1)
(
h
∘
g
∘
f
)
(
1
)
.
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