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Mathematics
Mathematics
Problem
Consider
h
(
x
)
=
ln
(
4
x
2
+
1
)
h(x)=\ln\bigl(4x^{2}+1\bigr)
h
(
x
)
=
ln
(
4
x
2
+
1
)
. Which of the following pairs
(
f
,
g
)
(f,\,g)
(
f
,
g
)
is NOT a valid decomposition of
h
h
h
as
g
∘
f
g\circ f
g
∘
f
? a)
f
(
x
)
=
x
2
,
g
(
u
)
=
ln
(
4
u
+
1
)
f(x)=x^{2},\; g(u)=\ln(4u+1)
f
(
x
)
=
x
2
,
g
(
u
)
=
ln
(
4
u
+
1
)
b)
f
(
x
)
=
2
x
,
g
(
u
)
=
ln
(
u
2
+
1
)
f(x)=2x,\; g(u)=\ln(u^{2}+1)
f
(
x
)
=
2
x
,
g
(
u
)
=
ln
(
u
2
+
1
)
c)
f
(
x
)
=
2
x
,
g
(
u
)
=
ln
(
4
u
2
+
1
)
f(x)=2x,\; g(u)=\ln(4u^{2}+1)
f
(
x
)
=
2
x
,
g
(
u
)
=
ln
(
4
u
2
+
1
)
d)
f
(
x
)
=
4
x
2
,
g
(
u
)
=
ln
(
u
+
1
)
f(x)=4x^{2},\; g(u)=\ln(u+1)
f
(
x
)
=
4
x
2
,
g
(
u
)
=
ln
(
u
+
1
)
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