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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
log
3
(
2
x
−
1
)
f(x)=\log_{3}(2x-1)
f
(
x
)
=
lo
g
3
(
2
x
−
1
)
and
g
(
x
)
=
4
x
+
2
g(x)=4^{x+2}
g
(
x
)
=
4
x
+
2
. a. (i) Find
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
and simplify your answer as far as possible. b. (ii) Calculate
(
f
∘
g
)
(
−
1
)
(f\circ g)(-1)
(
f
∘
g
)
(
−
1
)
. c. (iii) Determine the domain of
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
, writing your answer in interval notation.
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