Determine whether each function is even, odd, or neither.
1. f(x) = sqrt x^2 - 9
2. g(x) = |x-3|
3. f(x) = 1/2
4. f(x) = x/x²-1
5. g(x) = x + x^2

Answers

Answer 1

Answer:even,neither,odd,neither

Step-by-step explanation:I’m not explaining I just gave you the answers

Answer 2

1. [tex]f(x) = \sqrt{x^2 - 9}[/tex] is even.

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

3. f(x) = 1/2 is neither even nor odd.

4. [tex]f(x) = x / (x^2 - 1)[/tex] is odd.

5. [tex]g(x) = x + x^2[/tex] is neither even nor odd.

To determine whether each function is even, odd, or neither, we need to apply the definitions of even and odd functions:

1. An even function satisfies f(x) = f(-x) for all x in its domain.

2. An odd function satisfies f(x) = -f(-x) for all x in its domain.

Let's analyze each function:

1. [tex]f(x) = \sqrt{x^2 - 9}[/tex]

To determine if this function is even or odd, we need to check f(x) and f(-x):

[tex]f(x) = \sqrt{x^2 - 9}\\f(-x) = \sqrt{(-x)^2 - 9} = \sqrt{x^2 - 9}[/tex]

Since f(x) = f(-x), the function is even.

2. g(x) = |x - 3|

To determine if this function is even or odd, we need to check g(x) and g(-x):

g(x) = |x - 3|

g(-x) = |-x - 3|

Since |-x - 3| is not equal to |x - 3|, the function is neither even nor odd.

3. f(x) = 1/2

Since this is a constant function (not dependent on x), it is neither even nor odd.

4. [tex]f(x) = x / (x^2 - 1)[/tex]

To determine if this function is even or odd, we need to check f(x) and f(-x):

[tex]f(x) = x / (x^2 - 1)\\f(-x) = (-x) / ((-x)^2 - 1) = -x / (x^2 - 1)[/tex]

Since f(x) = -f(-x), the function is odd.

5. [tex]g(x) = x + x^2[/tex]

To determine if this function is even or odd, we need to check g(x) and g(-x):

[tex]g(x) = x + x^2\\g(-x) = -x + (-x)^2 = -x + x^2[/tex]

Since g(x) is not equal to g(-x), the function is neither even nor odd.

To know more about even:

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Answers

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What is an ellipse?

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.

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