MATHEMATICS MIDDLE SCHOOL

Which of the following is an odd function?

Answers

Answer 1

Answer:

Answer:

f(x) = -x is odd

Step-by-step explanation:

A function f is odd if f(-x) = -f(x) for all x in the domain of f. Then, let's check each of the functions.

1. f(x) = x^3 + 5x^2 + x

f(-x) = (-x)^3 + 5(-x)^2 + (-x) = -x^3 + 5x^2 - x

-f(x) = -(x^3 + 5x^2 + x) = -x^3 - 5x^2 - x

Given that f(-x) ≠ -f(x). The function f is not odd.

2. f(x) = sqrt(x)

f(-x) = sqrt(-x) (Imaginary number)

-f(x) = -sqrt(x)

Given that f(-x) ≠ -f(x). The function f is not odd.

3. f(x) = x^2 + x

f(-x) = (-x)^2 -x = x^2 - x

-f(x) = -x^2 - x

Given that f(-x) ≠ -f(x). The function f is not odd.

4. f(x) = -x

f(-x) = - (-x) = x

-f(x) = -(-x) = x

Given that f(-x) = -f(x). The function f is odd.

Answer 2

Answer:

Answer with Step-by-step explanation:

A function f is odd if:

f(-x)= -f(x) for all x in the domain of f

1. f(x)= $x^3+5x^2+x$

f(-x)= $(-x)^3+5(-x)^2-x$

= $-x^3+5x^2-x$

-f(x)= $-x^3-5x^2-x$

f(-x) ≠ -f(x)

So, function is not odd

2. f(x)=√x

f(-x)=√(-x)

= i√x

-f(x)= -√x

f(-x) ≠ -f(x)

So, function is not odd

3. f(x)= $x^2+x$

f(-x)= $(-x)^2-x$

= $x^2-x$

-f(x)= $-x^2-x$

f(-x) ≠ -f(x)

So, function is not odd

4. f(x)= -x

f(-x) = -(-x)

-f(x)=x

f(-x) = -f(x)

So, function is odd

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Answers

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Answers

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Answers

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Step-by-step explanation:

Answer:

Step-by-step explanation:

Hot dogs buns come in packages of 8 for the school picnic mr spencer bought 30 packages of hot dog buns . How many hot dog buns did he buy

Answers

Answer:

240 buns

Step-by-step explanation:

Hot dogs buns come in packages of 8.

Mr Spencer bought 30 packages of hot dog buns for the school picnic.

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Answers

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