Is y = sin3x + TaNx a periodic function? If so, what is the period?

Is y = sin3x + TaNx a periodic function? If so, what is the period?

f(x+2π)=sin(3x+6π)+tan(x+2π)=sin3x+tanx=f(x)
It's a periodic function, period 2 π

Is y = X. cosx bounded from negative infinity to positive infinity? When x approaches positive infinity, is this function infinite? Why?

Unbounded is certain, because you take any positive or negative number, I can take an X, so that x is larger (or smaller) than you take, and cosx is equal to one, which proves that unbounded, and the limit to the problem is not positive infinity or negative infinity (the definition of limit), so when x tends to infinity, it does not tend to infinity
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Is y = e ^ (- x) an odd function? Is y = SiNx + cosx a bounded function?

When y = e ^ (- x) x = 0, y = 1 is not an odd function
Y = SiNx + cosx = √ 2Sin (x + 45 °) is the range of bounded functions [- √ 2, √ 2]