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vesna_86 [32]
3 years ago
12

What is the inverse operation of division?

Mathematics
1 answer:
Stella [2.4K]3 years ago
8 0
The inverse operation of division is multiplication <span />
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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
A car uses 8 gallons of gasoline to travel 192 miles. How many gallons are used to go 144 miles? *
antiseptic1488 [7]

Answer:

6 gallons

Step-by-step explanation:

You can find this using the ration method.

If, 8 gallons : 192 miles

   x gallons : 144 miles

We must find the value of x, which is the number of gallons used to travel 144 miles.

Cross multiply the ratios.

192 x = 8 × 144

192 x = 1152

x = 1152 ÷ 192

x = 6

∴ It takes 6 gallons to travel 144 miles.

8 0
3 years ago
Subtracting 5 from each score in a distribution with a mean equal to 40 and a standard deviation equal to 3 will result in a sta
LenaWriter [7]

Adding or subtracting a constant from each value of a distribution changes the mean, but not the standard deviation.


The standard deviation will equal 3.

6 0
3 years ago
Rachel made a mosaic from different color rectangular tiles. Three tiles measured 312 inches by 3 inches. Six measured 4 inches
astraxan [27]
The answer is 10,344 hope this helps!
3 0
3 years ago
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Transform the following polar equation into an equation in rectangular coordinates: r=2 cos theta A. x + y = 2 B. y = 2x C. x =
Mila [183]
r=2\cos\theta
r^2=2r\cos\theta
\implies x^2+y^2=2x
x^2-2x+y^2=0
x^2-2x+1+y^2=1
(x-1)^2+y^2=1
8 0
3 years ago
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