Question

h(x)=5x^4-3x^2-2
h(-x)=?
I got 2x-2 for the answer, I don't get what I did wrong

Answer 1

You are suppose to have the same amount of terms in both h(x) and h(-x)

Answer 2

replace all the x's in h(x) with -x

Answer 3

now this can be cleaned up a little

Answer 4

\[h(-x)=5(-x)^4-3(-x)^2-2*\]

Answer 5

try to simplify (-x)^4

Answer 6

=x

Answer 7

well not exactly...

Answer 8

\[(-x)^4=(-1 \cdot x)^4=(-1)^4 \cdot x^4=?\]

Answer 9

1x?

Answer 10

x^4

Answer 11

yes x^4

Answer 12

and what does(-x)^2=?

Answer 13

x^2

Answer 14

\[h(-x)=5(-x)^4-3(-x)^2-2 \\ h(-x)=5(-1 \cdot x)^4-3(-1 \cdot x)^2-2 \\ h(-x)=5(-1)^4(x)^4-3(-1)^2(x)^2-2\\h(-x)=5(1)x^4-3(1)x^2-2\\h(-x)=5x^4-3x^2-2\]

Answer 15

So in this case h(-x) actually equals h(x)

Answer 16

Which implies a certain kinda symmetry

Answer 17

But the question was just what is h(-x)

Answer 18

hmm thats confusing, but i see what you did. thank you!

Answer 19

what part confuses you?

Answer 20

Could you find h(-x) if h(x)=x^3-5x^2+x-1

Answer 21

yea, i should have looked at it the same way

Answer 22

yes except here you actually have odd powers so ... if you have
\[(-x)^{even power}=x^{evenpower} \\ (-x)^{oddpower}=-x^{oddpower}\]

Answer 23

That will be a good thing to know for this type of thing

Answer 24

So what I'm saying is
example of that first thing I said \[(-x)^{20}=x^{20}\]
example of the second thing I said \[(-x)^{207}=-x^{207}\]

Answer 25

Notice the 20 was even and the 207 was odd

Answer 26

oh okay, i see

Answer 27

Let me know when you have found h(-x) for this new h(x) I made for you