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3 years ago

Solve the following absolute value inequality graphically: |x|-3>1.

Mathematics

1 answer:

Dovator [93]3 years ago

7 0

Answer:

x < -4 ∪ x > 4

Step-by-step explanation:

The absolute value function is shifted down 3 units. The solution space is values of x where y = |x|-3 is greater than 1. The solution is shown in red in the attachments, and the left and right (dashed) sides of the inequality are shown in blue.

I personally prefer to rewrite the inequality so the comparison is to <em>zero</em>. That is done in the second attachment, which rewrites it to ...

|x| -4 > 0

by subtracting 1 from both sides. It is often easier to read the values of x-intercepts than it is to read the coordinate values where lines cross each other.

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15 pts. Prove that the function f from R to (0, oo) is bijective if - f(x)=x2 if r- Hint: each piece of the function helps to "c

solniwko [45]

Answer with explanation:

Given the function f from R to $(0,\infty)$

f: $R\rightarrow(0,\infty)$

$-f(x)=x^2$

To prove that the function is objective from R to $(0,\infty)$

Proof:

$f:(0,\infty )\rightarrow(0,\infty)$

When we prove the function is bijective then we proves that function is one-one and onto.

First we prove that function is one-one

Let $f(x_1)=f(x_2)$

$(x_1)^2=(x_2)^2$

Cancel power on both side then we get

$x_1=x_2$

Hence, the function is one-one on domain [tex[(0,\infty)[/tex].

Now , we prove that function is onto function.

Let - f(x)=y

Then we get $y=x^2$

$x=\sqrt y$

The value of y is taken from $(0,\infty)$

Therefore, we can find pre image for every value of y.

Hence, the function is onto function on domain $(0,\infty)$

Therefore, the given $f:R\rightarrow(0.\infty)$ is bijective function on $(0,\infty)$ not on whole domain R .

Hence, proved.

3 0

3 years ago

write the slope - intercept equation of the line that passes through the point (6, "-1)" and has a slope of "-1/3"

andreev551 [17]

Answer:

-1 = 1/3 * 6 - 3

Step-by-step explanation:

So if it goes through point (6, -1) and has a slope of -1/3, all of this is parts of the slope intercept equal, Y = mx - B. You have the slope, which is m in the equation, y = -1/3 x - b. you already have a y and x which are the points passed, -1 = -1/3 * 6 - b, but this can't equal y, so you must have did it wrong, the only way this could equal y is if the slope wasn't negative, and in that case it would be -1 = 1/3 * 6 - 3. Because 1/3 * 6 is 2 and then subract 3 and you get -1.

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2 years ago

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The largest prime factor of twelve is

Masja [62]

Answer:

i know the smallest prime factor of 12 is 2

Step-by-step explanation:

step by step im sorry i not smart

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