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Algebraically determine whether the following functions are Eron. odd or Noither f(x) = x³ = x² + 4x + 2 f(x) = -x ² + 10 f(x) = √[x^4-x²] + 4​

User Sujith PS
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Answer: On the "Step by Step Explanation"

Explanation:

First, I think you meant to write “even”, “odd” or “neither” instead of “Eron”, “odd” or “Noither”. A function is even if f(-x) = f(x), odd if f(-x) = -f(x), and neither if it does not satisfy either condition.

To determine whether a function is even, odd or neither, we need to substitute -x for x in the function and simplify the expression. Then we need to compare the result with the original function.

Let’s do this for each function:

f(x) = x³ + x² + 4x + 2

f(−x)=(−x)3+(−x)2+4(−x)+2

f(−x)=−x3+x2−4x+2

This is not equal to f(x) or -f(x), so this function is neither even nor odd.

f(x) = -x² + 10

f(−x)=−(−x)2+10

f(−x)=−x2+10

This is equal to f(x), so this function is even.

f(x) = √[x^4-x²] + 4

f(−x)=(−x)4−(−x)2​+4

f(−x)=x4−x2​+4

This is also equal to f(x), so this function is also even.

User Thaleshcv
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