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Mathematics
Problem
Let
f
(
x
)
=
2
x
+
5
f(x)=2x+5
f
(
x
)
=
2
x
+
5
for all real
x
x
x
. Find the ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
so that
g
(
x
)
=
a
x
+
b
g(x)=ax+b
g
(
x
)
=
a
x
+
b
satisfies
f
(
g
(
x
)
)
=
x
f\bigl(g(x)\bigr)=x
f
(
g
(
x
)
)
=
x
for every real
x
x
x
. a)
(
1
2
,
−
2
)
(\tfrac12,-2)
(
2
1
,
−
2
)
b)
(
1
2
,
−
5
2
)
(\tfrac12,-\tfrac52)
(
2
1
,
−
2
5
)
c)
(
1
2
,
5
2
)
(\tfrac12,\tfrac52)
(
2
1
,
2
5
)
d)
(
2
,
−
5
2
)
(2,-\tfrac52)
(
2
,
−
2
5
)
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