Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

I
For each of the following functions find f(-x) and -f(x), then determine whether it
is even, odd or neither. Justify your answer.
f(x)=x^3-7/x
f(x)=|-x|
f(x)=25-x^3
f(x)=72-x^4

Sagot :

facundo3141592

By using the definition of even and odd functions, we will see that:

  • a) odd
  • b) even.
  • c) neither
  • d) even.

What is an odd and an even function?

A function f(x) is even if:

f(x) = f(-x)

And the function is odd if:

f(-x) = -f(x).

Now let's check it for all the given functions.

a) f(x) = x^3 - 7/x

  • -f(x) = -x^3 + 7/x
  • f(-x) = (-x)^3 - 7/(-x) = -x^3 + 7/x

So this function is odd.

b)  f(x) = |-x|

  • -f(x) = -|-x|
  • f(-x) = |-(-x)| = |x| = |-x|

This function is even.

c) f(x)=25-x^3

  • -f(x) = -25 + x^3
  • f(-x) = 25 - (-x)^3 = 25 + x^3

This function is neither odd nor even.

d) f(x) = 72-x^4

  • -f(x) = -72 + x^4
  • f(-x) = 72 - (-x)^4 = 72 - x^4 = f(x)

This function is even.

If you want to learn more about odd and even functions, you can read:

https://brainly.com/question/2284364

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.