Question

Using the definitions of odd and even functions , explain why y=sin x+1 is neither odd or even

Answer 1

This is neither because none of these:

`f(-x) = f(x)`

`f(-x) = -f(x)`

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:

`f(-x) = f(x)`

`f(- ( \pi )/(2) ) = 1 + sin(- ( \pi )/(2) ) = 1-1 = 0`

`f(-x) = -f(x)`

`f( ( \pi )/(2)) = 1+sin( ( \pi )/(2)) = 1+1 = 2`

As we can see, 0 ≠ 2. Hence, the function is neither odd nor even.