Question

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Answer 1

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:

brainly.com/question/2284364