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3 years ago

Which of the following pairs of functions are inverse’s of each other?

Mathematics

1 answer:

liubo4ka [24]3 years ago

5 0

The answers in C are inverses of each other.

In order to find the inverse of any equation, you simply switch the x and f(x) values and then solve for the new f(x). What it will result in is your new inverse function. If we do this for each of the problems above, only one will produce the second equation properly. See the work below for how to do it for C.

f(x) = 11x - 4 ---> Switch the x and f(x)

x = 11f(x) - 4 ----> Add 4 to both sides

x + 4 = 11f(x) ----> Divide both side by 11

$\frac{x+4}{11}$ = f(x) ----> Now put in the correct order

f(x) = $\frac{x+4}{11}$

Since our inverse matches the g(x) function, this means that C is the correct answer.

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marishachu [46]

Answer: The answer is F.

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2 years ago

What is the equation of a line perpendicular to:

Nataly [62]

Step-by-step explanation:

"perpendicular" means it creates a right angle (90°) with the original line.

a key element is the slope (the incline) of the line.

it is the factor of x (here 1/4 for the original line) and is defined as the ratio of "y coordinate change / x coordinate change" when going from one point on the line to another.

the given slope of 1/4 means that for every increase in x by 4 units y increases by 1 unit.

now if you want to draw a few random lines, and then draw lines that cross them with a right angle, you will see very quickly the relationship of the slopes of the crossing lines :

for the slope of the perpendicular line x and y of the original slope trade places (the ratio turns "upside-down") and the sign of the slope flips (if the original line goes up, then the perpendicular line goes down and vice versa. so + turns into -, and - into +).

so, our original slope 1/4 turns into -4/1 = -4.

we still have infinite possibilities to draw such a perpendicular line (more up or more down on the coordinate grid).

to finally "nail" one particular line we need to use the given point and solve for the y-intercept.

the general slope-intercept form is

y = ax + b

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so, using the slope (-4) and the point (2, 5) we have

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2 years ago

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Leto [7]

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2 years ago

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Delicious77 [7]

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Step-by-step explanation:

Since we have given that

Number of owls = 30

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If the number of owls and squirrels will continue to increase.

If there are 1000 squirrels, then the number of owls would be

$\dfrac{30}{45}=\dfrac{x}{1000}\\\\x=\dfrac{30\times 1000}{45}\\\\x=666.67\\\\x\approx 667$

Hence, there are 667 owls for every 1000 squirrels.

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2 years ago

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Akimi4 [234]

Answer:

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