Question - year 11 3u (1 Viewer)

[*girl04*]

hey im in year 11 and i just have a quick question

we are doing functions and you know how they can be odd, even or neither? how do you figure it out? because i always get odd or even as the answer even when it is neither

i am using f(-x) = f(x) for even

and f(-x) = -f(x) for odd

but i never come up with neither!

thanks!

 

[*girl04*]

an e.g.

my book says that f(x) = x + x squared is neither

but i get odd or even

 

[:: ck ::]

f(x) = x + x^2

f(-x) = -x + x^2

-f(x) = -(x+x^2)
= -x -x^2

none of these are equivalent so the function is neither odd or even

 

[CM_Tutor]

My advice would be to put in ALL of the working, ie:

f(x) = x + x²

So, f(-x) = (-x) + (-x)²
= (-1)x + [(-1)x]²
= -x + (-1)²x²
= -x + x²

Now, this is neither -f(x) = -(x + x²) nor f(x), and so the function is neither odd nor even.

Note: For simple polynomials, just look at the degrees of the terms to figure out the answer. If all degrees are even, then the function is even. If all degrees are odd, then the function is odd. If there are a mixture of odd and even degrees, then the function is neither odd nor even. Remember when doing this that a constant is a term in x⁰, and so should be thought of as having an even degree.

 

[*girl04*]

hey thanks guys! i think im getting it now