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11 days ago

5

Consider the graphs of f (x) = StartAbsoluteValue x EndAbsoluteValue + 1 and g (x) = StartFraction 1 Over x cubed EndFraction. T

he composite functions f(g(x)) and g(f(x)) are not commutative, based on which observation?

2 answers:

AnnZ [9K]11 days ago

7 0

Answer:

We have defined functions:

f(x) = IxI + 1

g(x) = 1/x^3.

Currently, it is evident that the composite functions are not commutative.

How can we demonstrate this?

To determine if two composite functions are commutative, the following must hold true:

f(g(x)) = g(f(x))

One could apply brute force (simply substituting values to see if the composite functions commute),

but I will opt for a more sophisticated approach.

There are two notable observations:

g(x) has a point of discontinuity at x = 0.

Thus:

f(g(x)) = I 1/x^3 I + 1

remains discontinuous at x = 0, whereas:

g(f(x)) = 1/(IxI + 1)^3

shows that the denominator IxI + 1 can never reach zero.

At this point, there is no discontinuity.

Consequently, the composite functions cannot be commutative.

Leona [9.2K]11 days ago

4 0

Answer: C The domains of f(x) and g(x) differ

Step-by-step explanation:

I got the answer right on Edgenuity

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What is the empirical formula of an oxide of chromium that is 48 percent oxygen by mass?

Svet_ta [9500]

Answer:

CrO₃.

Step-by-step explanation:

First, we will find the chromium percentage in the oxide by using the following process:

Oxygen (O) = 48%

Chromium (Cr) =?

The oxide consists solely of chromium and oxygen, and its chromium percentage is calculated as:

Cr = 100 – percentage of oxygen

Cr = 100 – 48

Cr = 52%

Next, we will determine the empirical formula for the oxide:

Chromium (Cr) = 52%

Oxygen (O) = 48%

Now, we divide by their molar mass:

Cr = 52/52 = 1

O = 48/16 = 3

Now, divide by the lowest value:

Cr = 1/1 = 1

O = 3/1 = 3

Thus, the empirical formula for the oxide is CrO₃.

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1 month ago

A periscope is 5 feet above the surface of the ocean. Through it can be seen a ship that rises to 50 feet above the water. To th

PIT_PIT [9117]

The maximum distance visible on Earth is calculated using the formula $d=\sqrt{8,000h_1} + \sqrt{8,000h_2}$

$h_1$ = your initial height and $h_2$ = your secondary height

In this case, $h_1=5$ represents the height of the periscope and $h_2=50$ denotes the height of the ship, leading us to a distance of 832.45553203368 feet. However, rounding to the nearest mile yields the answer as $11^a^0$

If there are any discrepancies, please inform me and I will recalculate!

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17 days ago

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given b

PIT_PIT [9117]

Answer:

The amount of ovens that must be produced in a week to earn a $1610 profit is 70.

Step-by-step explanation:

Given:

A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:

$P=\frac{1}{10}x(300-x)$

with 0 ≤ x ≤ 200.

The target profit is $1610

So, set P = 1610, then solve for x:

$1610=\frac{1}{10}x(300-x)$

Multiply both sides by 10:

$1610\cdot \:10=\frac{1}{10}x\left(300-x\right)\cdot \:10$

$16100=x\left(300-x\right)$

$16100=300x-x^2$

$-x^2+300x-16100=0$

Next, factor the quadratic:

$(x-70)(x-230)=0$

Solving for x gives:

$x=70,x=230$

Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.

Hence, the valid solution is x=70.

Therefore, to achieve a $1610 profit, the manufacturer must produce 70 ovens weekly.

7 0

1 month ago

Josh Josh estimates the height of his desk what is the reasonable estimate

PIT_PIT [9117]

The estimated height would be around 3 feet, which would correspond to a level that is approximately at waist height.

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1 month ago

Which are the roots of the quadratic function f(b) = b2 – 75? Select two options. b = 5 StartRoot 3 EndRoot b = Negative 5 Start

zzz [9080]

Answer:

b = 5√3

b = -5√3

Step-by-step explanation:

We have

$f(b)=b^{2}-75$

Keep in mind, the root of a function corresponds to the value of x at which the function's output is zero.

In this case

The roots of the equation are the b values for which f(b) equals zero.

Thus

For f(b)=0

$b^{2}-75=0$

$b^{2}=75$

Take the square root of both sides

$b=(+/-)\sqrt{75}$

Now simplify

$b=(+/-)5\sqrt{3}$

$b=5\sqrt{3}$ and $b=-5\sqrt{3}$

So we find that

b = 5√3

b = -5√3

8 0

26 days ago

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