Question

Is y=(x+5)/(x-3)(x+1) even, odd or neither?

Answer 1

Is this \[y=\frac{x+5}{(x-3)(x+1)}\]

Answer 2

neither

Answer 3

Yes, I mean't y=(x+3)/((x-3)(x+1))

Answer 4

I also thought it was neither, because it has even and odd exponents, is my reasoning right or am I missing something?

Answer 5

This is neither even nor odd

Answer 6

\[y=\frac{x+5}{(x-3)(x+1)}\] is neither. you can check using the definition, or you can just pick a number for x. i pick 2
\[f(2)=\frac{2+5}{(2-3)(2+1)}=\frac{7}{-3}\] now i try with xm -2 and get
\[\frac{-2+5}{(-2-5)(-2+1)}=\frac{3}{7}\] so not even or odd. if it was even i would get
\[\frac{7}{-3}\] and if it were i should get \[\frac{7}{3}\]

Answer 7

be careful about the exponents.
\[\frac{x^2-4}{x^3}\] for example is odd, even though it has both even and odd exponents

Answer 8

that is because
\[x^2-4\] it even and
\[x^3\] is odd and
\[\frac{even}{odd}\] is odd.

Answer 9

the real check is replacing x by -x and see if you get the same thing back. if so even. if you get the negative of the function back, it is odd. if you get neither, then neither even nor odd

Answer 10

so for your original example you should check
\[\frac{-x+5}{(-x-3)(-x+1)}\] and you will see that this is not
\[\frac{x+5}{(x-3)(x+1)}\] nor it it
\[-\frac{x+5}{(x-3)(x+1)}\]

Answer 11

oh hello! did you stay up all night again?

Answer 12

\[f(-x)=\frac{-x+5}{(-x-3)(-x+1)}=\frac{-x+5}{(-1)(x+3)(-1)(x-1)}=\frac{-x+5}{(x+3)(x-1)}\]

Answer 13

yep

Answer 14

beat you to it!

Answer 15

i am off. see you later

Answer 16

im a master :)

Answer 17

\[\color{red}{\huge{\text{my myinninaya is a master!}}}\]

Answer 18

except she is about to make a mistake. because
\[-f(-x)\] is not what you wrote

Answer 19

\[-f(x)=\frac{-(x+5)}{(x-3)(x+1)}\]

Answer 20

if f(-x)=f(x) then it is even
if f(-x)=-f(x) then it is odd
if we have neither of the above ,it is neither
so neither