If g(x) is an even function then sin(g(x)) is also even. True or False? Explain.?

Answer 1

True. In fact, we may make the more general statement that if f is any function whatsoever and g(x) is even then f(g(x)) is even. Recall that a function g is even iff g(-x) = g(x). But then f(g(-x)) = f(g(x)), so f∘g is even.