Answer
No.
Work Step by Step
A function $f$ is a one-to-one function if different values of the domain correspond to different values of the range.
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Given that $f(x)=c$, for some constant c,
we take any two different values from the domain, say 0 and 1,
and find that
$f(0)=c,$
$f(1)=c$,
that is, that they have same function values.
So, f is not a one-to-one function.
