By using the definition of even and odd functions, we will see that:
- a) odd
- b) even.
- c) neither
- d) even.
<h3>
What is an odd and an even function?</h3>
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:
brainly.com/question/2284364
