Answer:
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
[tex]f\left(-x\right)=|x+3|[/tex]
and
[tex]-f\left(x\right)=-\left|x-3\right|[/tex]
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.
