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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Determine algebraically whether the given function is even, odd, or neither: f(x) = x5 - x3 + x.
Functions are very important concepts in mathematics. There are many types of functions, which include even functions, odd functions, or neither odd nor even functions.
Answer: The function f(x) = x5 - x3 + x is an odd function.
Let's understand the solution in detail.
Explanation:
To check for odd functions, we have to verify whether f(-x) = -f(x).
We have f(x) = x5 - x3 + x.
Now, we find f(-x):
f(-x) = (-x)5 - (-x)3 + (-x)
f(-x) = -x5 + x3 - x
Now, we find -f(x):
-f(x) = -(x5 - x3 + x)
-f(x) = -x5 + x3 - x
Hence, we see that f(-x) = -f(x)
Thus, we conclude that the given function f(x) = x5 - x3 + x is an odd function.
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