If the definition field of odd function f (x) = xcosx + C is [a, b], then a + B + C = 0, find the concrete process

If the definition field of odd function f (x) = xcosx + C is [a, b], then a + B + C = 0, find the concrete process

Yes, the odd function f (0) = 0
0cos0+C=0
c=0
And the interval is symmetric, so a + B = 0
a+b+c=0

If the definition field of odd function f (x) = SiNx + C is [a, b], then a + B + C=______ ．

∵ the definition domain of odd function f (x) = SiNx + C is [a, b], ∵ a + B = 0, and f (0) = sin0 + C = 0. If C = 0, then a + B + C = 0, so the answer is: 0

If the odd function f (x) is x > 0, f (x) = SiNx cosx to find X

When X0
So f (- x) = sin (- x) - cos (- x)
=-sinx-cosx
Because it's an odd function
So f (- x) = - f (x)
So - f (x) = - SiNx cosx
So f (x) = SiNx + cosx

If the definition field of odd function f (x) = SiNx + C is [a, b], then a + B + C=______ ．

∵ the definition domain of odd function f (x) = SiNx + C is [a, b], ∵ a + B = 0, and f (0) = sin0 + C = 0. If C = 0, then a + B + C = 0, so the answer is: 0