Testing for symmetry question

[Juxtaposition109]

If given the function (-x^3) / (5x^2+7) and told to determine algebraically if it is even, odd, or neither, I know that to determine if it is even I have to set F(x) to F(-x). However since there is already a (-x) in the equation at (-x^3) do I replace the -x in -x^3 w/ a positive x, or do I leave the equation at its original -x^3 and test? Thx for any help.

 

[Deleted member 4993]

If given the function (-x^3) / (5x^2+7) and told to determine algebraically if it is even, odd, or neither, I know that to determine if it is even I have to set F(x) to F(-x). However since there is already a (-x) in the equation at (-x^3) do I replace the -x in -x^3 w/ a positive x, or do I leave the equation at its original -x^3 and test? Thx for any help.

\(\displaystyle \displaystyle{f(-x) \ = \ \dfrac{-[(-x)^3]}{5*[(-x)^2]+7}}\)

Continue....

 

[Juxtaposition109]

\(\displaystyle \displaystyle{f(-x) \ = \ \dfrac{-[(-x)^3]}{5*[(-x)^2]+7}}\)

Continue....

Thank you very much

 

[Juxtaposition109]

The answer key on this one says it's an odd function. I am confused on this.

Wouldn't the -x^3 become -x and then -x(-) would make the numerator positive. Then the -x inserted in the bottom makes the denominator positive also. Thus the function comes out the same as before and is thus an even function?

 

[stapel]

The answer key on this one says it's an odd function. I am confused on this.

Wouldn't the -x^3 become -x...

Why would the "cubed" disappear? Why would the "minus on (x-cubed)" become "(something??) on (minus on x)"?

...and then -x(-)

What does this even mean? :shock:

Please reply showing your steps (rather than making cryptic reference to them), explaining why you are doing what you're doing. Thank you!

 

[Deleted member 4993]

The answer key on this one says it's an odd function. I am confused on this.

Wouldn't the -x^3 become -x and then -x(-) would make the numerator positive. Then the -x inserted in the bottom makes the denominator positive also. Thus the function comes out the same as before and is thus an even function?

Your original f(x) had a negative numerator.

Your f(-x) has a positive numerator.

Now decide.....

 

[pka]

If given the function (-x^3) / (5x^2+7) and told to determine algebraically if it is even, odd, or neither, I know that to determine if it is even I have to set F(x) to F(-x). However since there is already a (-x) in the equation at (-x^3) do I replace the -x in -x^3 w/ a positive x, or do I leave the equation at its original -x^3 and test? Thx for any help.

\(\displaystyle \Large f(-x)=\dfrac{-(-x)^3}{5(-x)^2+7}=\dfrac{x^3}{5x^2+7}=-f(x)\)