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Mathematics
Problem
For a real parameter
k
k
k
, consider the function
f
k
:
R
→
R
f_{k}:\mathbb R\to\mathbb R
f
k
:
R
→
R
defined by
f
k
(
x
)
=
k
x
3
+
x
f_{k}(x)=kx^{3}+x
f
k
(
x
)
=
k
x
3
+
x
. (a) Determine all real values of
k
k
k
for which
f
k
f_{k}
f
k
is injective. (b) For the values of
k
k
k
found in part (a), state whether
f
k
f_{k}
f
k
is surjective and hence invertible.
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