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Mathematics
Mathematics
Problem
For
k
∈
R
k\in\mathbb{R}
k
∈
R
, define
f
k
:
R
→
R
f_k:\mathbb{R}\to\mathbb{R}
f
k
:
R
→
R
by
f
k
(
x
)
=
k
x
3
+
(
k
−
1
)
x
f_k(x)=kx^{3}+(k-1)x
f
k
(
x
)
=
k
x
3
+
(
k
−
1
)
x
. Find all real values of
k
k
k
for which
f
k
f_k
f
k
is one-to-one on
R
\mathbb{R}
R
.
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