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GarryVolchara [31]
4 years ago
12

25. Algebraically determine whether the function k(x) = x6 - x2 + 7 is odd, even, or neither. Explain your

Mathematics
1 answer:
alekssr [168]4 years ago
7 0

Answer: The function is EVEN.

Step-by-step explanation:

For this exercise it is important to remember that:

1. A function f(x) is even if and only if:

f(-x) = f(x) for all "x"

2. A function f(x) is odd if and only if:

f(-x) = -f(x) for all "x"

So knowing that, and given the following function k(x):

k(x)=x^6 - x^2 + 7

You can plug -x in for "x", order to know if this is even. Then, you get:

k(-x)=(-x)^6 - (-x)^2 + 7\\\\k(-x)=x^6-x^2+7

Therefore, since:

f(-x) = f(x)

You can determine that that the given function k(x)=x^6 - x^2 + 7 is Even.

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Step-by-step explanation:

Given expression:

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Problem;

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