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jekas [21]
3 years ago
8

If f(x)= x^-2, and g(x)=3x-1 whats the domain of f(g(x))?

Mathematics
1 answer:
andrey2020 [161]3 years ago
5 0
4 and 7 and 8 and 9 and10
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Each week, you drive 150 miles. Your car gets 25 miles to the gallon, and gas prices are $3 per gallon. How much gas money will
Jet001 [13]
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3 0
3 years ago
WILL MARK BRAINLIEST <br><br> what is the domain of (f/g) (x)?
tatyana61 [14]

Given that f(x) = \sqrt{7-x} and g(x) = \sqrt{x + 2}, we can say the following:

\Bigg(\dfrac{f}{g}\Bigg)(x) = \dfrac{f (x)}{g(x)} = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}


Now, remember what happens if we have a negative square root: it becomes an imaginary number. We don't want this, so we want to make sure whatever is under a square root is greater than 0 (given we are talking about real numbers only).


Thus, let's set what is under both square roots to be greater than 0:

\sqrt{7 - x} \Rightarrow 7 - x \geq 0 \Rightarrow x \leq 7

\sqrt{x + 2} \Rightarrow x + 2 \geq 0 \Rightarrow x \geq -2


Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.

x \leq 7 \,\,\cup x \geq -2 = \boxed{-2 \leq x \leq 7}


Now, let's look back at the function entirely, which is:

\Bigg( \dfrac{f}{g} \Bigg)(x) = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}

Since \sqrt{x + 2} is on the bottom of the fraction, we must say that \sqrt{x + 2} \neq 0, since the denominator can't equal 0. Thus, we must exclude \sqrt{x + 2} = 0 \Rightarrow x + 2 = 0 \Rightarrow x = -2 from the domain.


Thus, our answer is Choice C, or \boxed{ \{ x | -2 < x \leq 7 \}}.


<em>If you are wondering why the choices begin with the x | symbol, it is because this is a way of representing that x lies within a particular set.</em>

6 0
3 years ago
What is the area of a parallelogram if the coordinates of its vertices are (0, -2), (3, 2), (8,2), and (5,-2)?
Llana [10]

Answer:

The area of the parallelogram is 20 units²

Step-by-step explanation:

* Lets explain how to solve the problem

- The vertices of the parallelogram are (0 , -2) , (3 , 2) , (8 , 2) , (5 , -2)

- The side joining the points (0 , -2) and (5 , -2) is a horizontal side

  because the points have same y-coordinates

- The side joining the points (3 , 2) and (8 , 2) is a horizontal side

  because the points have same y-coordinates

∴ These two sides are parallel bases of the parallelogram

∵ The length of any horizontal side = x2 - x1

∴ The length of the side = 5 - 0 = 5 <em>or</em> 8 - 3 = 5

∴ The length of one base of the parallelogram is 5 units

- The height of this base is the vertical distance between these two

  parallel bases

∵ The length of any vertical distance = y2 - y1

∵ y2 = 2 and y1 = -2 ⇒ the y-coordinates of the parallel bases

∴ The length of the vertical distance = 2 - (-2) = 2 + 2 = 4 units

∵ This vertical distance between the two parallel bases is the height

  of these bases

∴ The height of the parallelogram is 4 units

- The area of the parallelogram = base × height

∵ The base = 5 units and the height = 4 units

∴ The area = 5 × 4 = 20 units²

* The area of the parallelogram is 20 units²

7 0
3 years ago
Mrs. Walters drove 360 miles of gas on 25 gallons of gas. Mr. Walters drive 480 miles on 32 gallons of gas. A. find the mileage
NikAS [45]
A.360 / 25= 14.4
B. 480 / 32= 15

B Is getting better mileage 
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3 0
3 years ago
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