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3 years ago

Identify the domain of the function

Mathematics

2 answers:

sertanlavr [38]3 years ago

7 0

The answer is C. is right

Roman55 [17]3 years ago

4 0

Answer:

C) (-4, 4]

Step-by-step explanation:

We have been given a graph of the function as shown in the picture. Now using that graph, we need to find the domain of the function and match with the given choices to find the correct domain.

Where given choices are :

A) [-4, 4)

B) [-4, 4]

C) (-4, 4]

D) (-4, 4)

Remember that we use ( or ) for open circle. and [ or ] for close circle.

Hence correct domain is

C) (-4, 4]

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3 years ago

How derivative of this absolute value function is like this!

Daniel [21]

Recall the definition of absolute value.

$|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}$

When $x$ ,

$|x| = x \implies \dfrac{d|x|}{dx} = 1$

When $x$ ,

$|x| = -x \implies \dfrac{d|x|}{dx} = -1$

The derivative does not exist at $x=0$ , since the one-sided limits

$\displaystyle \lim_{x\to0^-} f'(x) = -1$

and

$\displaystyle \lim_{x\to0^+} f'(x) = +1$

do not match.

So the derivative of $|x|$ is

$\dfrac{d|x|}{dx} = \begin{cases} 1 & \text{if } x > 0 \\ -1 & \text{if } x < 0 \\ \text{undefined} & \text{if } x = 0\end{cases}$

Now we can write this as

$\dfrac{d|x|}{dx} = \dfrac x{|x|} = \dfrac{|x|}x$

since

$x > 0 \implies |x| = x \implies \dfrac{|x|}x = \dfrac xx = 1$

and

$x < 0 \implies |x| = -x \implies \dfrac{|x|}x = -\dfrac xx = -1$

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1 year ago