Is the Combination of Sin Functions an Even Function?

[yungman]

Is

$$f(x)=\sin[a(b+|x|)]\;\hbox{ and }\; g(x)=\sin[a(b-|x|)]$$

Both EVEN function?

It looks even function to me even though it's a sine function( odd function), but the |x| make it an even function where f(-x)=f(x).

 

[CompuChip]

Yes, f(-x) = f(x) is the definition of an even function, and as you noted it satisfies that definition. To verify you can plot it and note that it is symmetric around the y-axis.

 

[HallsofIvy]

If f is any function whatsoever, then f(|x|) is an even function.

 

[yungman]

Thanks for the response.