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Mathematics
Mathematics
Problem
For
x
≠
1
x\neq 1
x
=
1
, let
f
(
x
)
=
m
x
+
2
x
−
1
f(x)=\dfrac{m x+2}{x-1}
f
(
x
)
=
x
−
1
m
x
+
2
, where
m
m
m
is a constant. Given that
f
(
3
)
=
1
f(3)=1
f
(
3
)
=
1
and
(
f
−
1
)
′
(
1
)
=
−
2
(f^{-1})'(1)=-2
(
f
−
1
)
′
(
1
)
=
−
2
, determine the value of
m
m
m
.
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