Determine whether each function is even, odd, or neither. f(x) = Vr²9

g(x) = |x-31

f(x) =

g(x) = x + x2

Please check the explanation.

Step-by-step explanation:

Even Functions:

The function is unchanged when it is reflected about the y-axis.

i.e.

f(-x) = f(x)

Odd Functions:

The function is unchanged when it is rotated 180° about the origin.

i.e.

f(-x) = -f(x)

Neither Functions:

f(-x) ≠ -f(x)

Let us check the given functions:

plug –x in for x

f(-x) = V(-x)²9

f(-x) = Vx²9

f(-x) = f(x)

Therefore, the function f(x) = Vx²9 is even function.

plug –x in for x

as

and

so

f(-x) ≠ f(x)

f(-x) ≠ -f(x)

Thus,

g(x) = |x-3| is neither an even nor an odd function.

plug –x in for x

g(-x) = (-x) + (-x)²

g(-x) = -x + x²

g(-x) = -(x-x²)

so

f(-x) ≠ f(x)

f(-x) ≠ -f(x)

Thus, it is neither an even nor an odd function.

Thus,

g(x) = x + x² is neither an even nor an odd function.

4th option is correct xy=-10

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answer: options

step-by-step explanation: