Question

State whether each of the following is an odd function, an even function or neither an even nor an off function

a) G(x)=x/x^4 - 4
b) k(x)=3x -|x|

Answer 1

Find G(-x)
by replacing x in G(x) by -x.
If G(-x) = G(x), then the function is even
If G(-x) = -G(x), then the function is odd
else neither.
same for K(x)

Answer 2

could u find G(-x) ?

Answer 3

No, I need help finding G(-x)

Answer 4

wherever u se 'x' in G(x), replace it by -x.

Answer 5

I'm even more confused. Please simplify it for me

Answer 6

for odd function f(x)=-f(-x)
for even function f(x)=f(-x)

Answer 7

That is exactly the same thing @hartnn said.

Answer 8

Could please help me solve at least one so i may use it as a guide?

Answer 9

@calculusfunctions @shunyao I guess my question i dont know how to solve it, pls

Answer 10

First replace every x in the equation with -x. What do you get?

Answer 11

G(-X)=-x/x^4-4
and
K(-x)= -3x+|x|

Answer 12

@odehye that's not clear! Answer my question is the equation I wrote correct or not?

Answer 13

@shunyao giving out answers is not helpful. Teach, explain, but don't just write the solutions. Please delete that!

Answer 14

@calculusfunctions not helpful ?

Answer 15

@shunyao yes!

Answer 16

@calculusfunctions i deleted it, you may show us your correct steps

Answer 17

First @odehye I need you to answer me. Is the first equation\[G(x)=\frac{ x }{ x ^{4}-4 }\]the correct equation?

Answer 18

yes

Answer 19

OK so then

Step 1: replace x with negative x. In other words, G(-x) = ?

Answer 20

If you don't know then don't be ashamed to just tell me.

Answer 21

I dont

Answer 22

@calculusfunctions replace x with negative x that is just what i did

Answer 23

OK then I appreciate your honesty. So suppose we have\[F(x)=\frac{ x -4 }{ x ^{2}-2x+16}\]}\]then \[F(-x)=\frac{ -x -4 }{ (-x)^{2}-2(-x)+16 }\]Do you see what I did? Can you follow this example to now tell me what G(-x) would be?

Answer 24

@shunyao I know. I didn't say your answer was incorrect. I just said you should be explaining and thus guiding the person asking the question to the correct solution.

Answer 25

@odehye you still don't understand?

Answer 26

G(-x)=-x/-x^4-4

Answer 27

@odehye do you not see my example and how the brackets are used?

Answer 28

Please try again!

Answer 29

For example, in my example the next step would be\[F(-x)=\frac{ -x -4 }{ x ^{2}+2x +16 }\]Do you see?

Answer 30

yes

Answer 31

OK then once again G(-x) = ?

Answer 32

@odehye