Thread: What does -f(x) mean? Is it the same thing as f(-x)?

So, In my precalc class we're learning whether or not a function is odd. And I keep on seeing this function notation -f(x) how do i evaluate it, is it just the opposite of the function? or is it just -1[f(x)]?

And what about if i'm trying to find out if a conic section is symmetrical to the origin, for instance an equation like x^2 + y^2 = 25, how do I do this -f(x) on an equation in which y isn't separated from the rest of the variables?

Originally Posted by glambeth

So, In my precalc class we're learning whether or not a function is odd. And I keep on seeing this function notation -f(x) how do i evaluate it, is it just the opposite of the function? or is it just -1[f(x)]?

And what about if i'm trying to find out if a conic section is symmetrical to the origin, for instance an equation like x^2 + y^2 = 25, how do I do this -f(x) on an equation in which y isn't separated from the rest of the variables?

I think this should help: Even and odd functions - Wikipedia, the free encyclopedia

I understand most of the stuff on that aforementioned wikipedia aritcle, however, I don't understand how to evaluate -f(x) of a function. Care to elucidate that to me?

Originally Posted by glambeth

I understand most of the stuff on that aforementioned wikipedia aritcle, however, I don't understand how to evaluate -f(x) of a function. Care to elucidate that to me?

Yes.

If f(x)=x^2+5x then -f(x)=-(x^2+5x)=-x^2-5x; if g(x)=sin(x) then -g(x)=-sin(x)

Originally Posted by glambeth

I understand most of the stuff on that aforementioned wikipedia aritcle, however, I don't understand how to evaluate -f(x) of a function. Care to elucidate that to me?

Here is an example.
Suppose that
Now

Whereas,

Originally Posted by glambeth

So, In my precalc class we're learning whether or not a function is odd. And I keep on seeing this function notation -f(x) how do i evaluate it, is it just the opposite of the function? or is it just -1[f(x)]?

And what about if i'm trying to find out if a conic section is symmetrical to the origin, for instance an equation like x^2 + y^2 = 25, how do I do this -f(x) on an equation in which y isn't separated from the rest of the variables?

Then, or

I like to say that -f(x) is f(x) reflected around the x-axis.

Originally Posted by pickslides

I like to say that -f(x) is f(x) reflected around the x-axis.

And f(-x) is f(x) reflected about the y-axis.

-f(x) is indeed (-1)(f(x)). f(-x) is f applied to -x.

for example:

, this function is even.

.

another example: .

. this function is odd.