Question

How do you determine if `F(x)= cos (sin x)` is an even or odd function?

Answer 1

A function `g` is said to be even, provided that `g(–x) = g(x)`, for all x.

A function `f` is said to be odd, provided that `f(–x) = –f(x)`, for all x.

Now we have that

`F(-x)=cos(sin(-x))=cos(-sinx)=cos(sinx)=F(x)` hence `F` is even.

Such functions have graphs that are symmetric about the y-axis as can be seen in the graph below