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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

Answer :

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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

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