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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
k
x
2
+
1
f(x)=k x^{2}+1
f
(
x
)
=
k
x
2
+
1
, where
k
k
k
is a constant. Given that
f
(
2
)
=
5
f(2)=5
f
(
2
)
=
5
and
(
f
−
1
)
′
(
5
)
=
1
4
(f^{-1})'(5)=\dfrac{1}{4}
(
f
−
1
)
′
(
5
)
=
4
1
, determine the value of
k
k
k
.
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