This is neither because none of these:
[tex]f(-x) = f(x)[/tex]
[tex]f(-x) = -f(x)[/tex]
I'm going to plug in π/2 to check if the odd and even function definition work for this problem or not. Let's do that:
[tex]f(-x) = f(x)[/tex]
[tex]f(- \frac{ \pi }{2} ) = 1 + sin(- \frac{ \pi }{2} ) = 1-1 = 0[/tex]
[tex]f(-x) = -f(x)[/tex]
[tex]f( \frac{ \pi }{2}) = 1+sin( \frac{ \pi }{2}) = 1+1 = 2 [/tex]
As we can see, 0 ≠ 2. Hence, the function is neither odd nor even.
