# Is this an even function?

1. May 11, 2013

### 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).

Last edited: May 11, 2013
2. May 11, 2013

### 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.

3. May 11, 2013

### HallsofIvy

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

4. May 11, 2013

### yungman

Thanks for the response.