Trying a new in 12.2 command FunctionInjective
, I execute
FunctionInjective({Sin(x)^2, Element(x, Integers)}, x)
False
and
FunctionInjective({Cos(x)^2, Element(x, Integers)}, x)
True
Both function are even on the reals, so both outputs should be False
as the output of
DiscretePlot(Cos(x)^2, {x, -8, 8})
shows,
How to explain this difference?
I try to present Cos(x)^2
as Sin(Pi/2 - x)^2
and (1+Cos(2x))/2
, but
the outputs of
FunctionInjective({Sin(Pi/2 - x)^2, Element(x, Integers)}, x)
and
FunctionInjective({(Cos(2*x) + 1)/2, Element(x, Integers)}, x)
still are True
.