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.