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NARA [144]
2 years ago
14

Suppose that the function f has domain all real numbers. Determine whether each function can be classified as even or odd. Expla

in.
a) g(x)= [f(x) + f(-x)]/2
b) h(x)= [f(x) – f(-x)]/2
Mathematics
1 answer:
dybincka [34]2 years ago
6 0

Answer:

a.Even

b.Odd

Step-by-step explanation:

We are given that function f has domain all real numbers .

We have to find that given function is even or odd

a.g(x)=\frac{f(x)+f(-x)}{2}

We know that if function is even then f(x)=f(-x) and if function is odd then f(x)\neq f(-x)

Replace x by -x then we get

g(-x)=\frac{f(-x)+f(x)}{2}=g(x)

Therefore, function is even .

b.h(x)=\frac{f(x)-f(-x)}{2}

Replace x by -x

Then we get h(x)=\frac{f(-x)-f(x)}{2}=-\frac{f(x)-f(-x)}{2}

h(x)\neq h(-x)

Hence, function is odd.

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Work Shown:

Use the pythagorean theorem to find x

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Answer:

{-2, -14, -26, -50}

Step-by-step explanation:

The range of the function is the function evaluated at each point of the given domain. So to find the range of the function we need to find the value of the function for each point in the domain:

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f(-8)=-2

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The second value of the range is -14

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Th third values of the range is -26

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The fourth and last value of the range is -50

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3 years ago
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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

According to the information given in the exercise, the value of "x" is:

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When you substitute the given value of "x" into the last expression and then  you evaluate, you get:

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2 years ago
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