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Mathematics
Problem
Let
f
f
f
be defined by
f
(
x
)
=
5
x
−
2
f(x)=5^{x-2}
f
(
x
)
=
5
x
−
2
. (a) Find the inverse function
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
. (b) State the domain and range of
f
f
f
and of
f
−
1
f^{-1}
f
−
1
. (c) Verify by composition that
f
(
f
−
1
(
x
)
)
=
x
f\bigl(f^{-1}(x)\bigr)=x
f
(
f
−
1
(
x
)
)
=
x
for all
x
x
x
in the domain of
f
−
1
f^{-1}
f
−
1
.
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