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3 years ago

Which of the following pairs of functions are inverses of each other?

Mathematics

1 answer:

AnnyKZ [126]3 years ago

4 0

Answer:

Step-by-step explanation:

Rearrange each function to solve for x.

Switch x and y,

The resulting equation is the inverse function.

f(x) = y = 5+x

x = y-5

y = x-5

f⁻¹(x) = x-5

g(x) = 5-x ≠ f⁻¹(x)

g(x) is not the inverse of f(x).

:::::

f(x) = y = 2x-9

x = (y+9)/2

y = (x+9)/2

f⁻¹(x) = (x+9)/2

g(x) = (x+9)/2 = f⁻¹(x)

g(x) is the inverse of f(x).

:::::

f(x) = y = 2/x - 6

x = 2/(y+6)

y = 2/(x+6)

f⁻¹(x) = 2/(x+6)

g(x) = (x+6)/2 ≠ f⁻¹(x)

:::::

f(x) = y = x/3 + 4

x = 3y - 12

y = 3x - 12

f⁻¹(x) = 3x - 12

g(x) = 3x - 4 ≠ f⁻¹(x)

g(x) is not the inverse of f(x).

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Which of the following is the simplified form of the expression -x(x - y) + 4xy - x2?

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-x+xy +4xy-x2
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3 years ago

Which expression is equivalent to 144 Superscript three-halves? 216 1,728 RootIndex 3 StartRoot 12 EndRoot RootIndex 3 StartRoot

Afina-wow [57]

Question:

Which expression is equivalent to 144^(3/2)

Answer:

1728

Step-by-step explanation:

The options are not well presented. However, this is the solution to the question.

Given:

144^(3/2)

Required:

Find Equivalent.

We start my making use of the following law of logarithm.

A^(m/n) = (A^m)^1/n

So,

144^(3/2) = (144³)^½

Another law of indices is that

A^½ = √A

So,

144^(3/2) = (144³)^½ = √(144³)

144³ can be expanded as 144 * 144 * 144.

This gives

144^(3/2) = √(144 * 144 * 144)

The square root can then be splitted to

144^(3/2) = √144 * √144 * √144

144^(3/2) = 12 * 12 * 12

144^(3/2) = 1728.

Hence, the equivalent of 144^(3/2) is 1728

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3 years ago

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A man starts walking north at 5 ft/s from a point P. Five minutes later a woman starts walking south at 6 ft/s from a point 500

aev [14]

Check the picture below.

the man is going North, and he has a rate of 5 f/s, she's going south, 500 miles from P, the green distance, and she's going 6 f/s.

by the time she started walking, he already had been walking for 5 minutes, or 300 seconds, since he's going 5 f/s, then he had already covered 1500 feet by then.

after that, they both walked for 15 minutes more or 900 seconds, and for her that means 5400 feet, whilst for him going slower means 4500 feet, as you see in the picture.

since he's going North and she's going South, dy/dt is the combined rates, as you see there.

now, let's use the pythagorean theorem, bearing in mind that the green 500 feet are constant all the while, that matters because the derivative of a constant is 0.

$\bf r^2=x^2+y^2\stackrel{chain~rule}{2r\cfrac{dr}{dt}}=0+\stackrel{chain~rule}{2y\cfrac{dy}{dt}}\implies \cfrac{dr}{dt}=\cfrac{2y}{2r}\cdot \cfrac{dy}{dt}
\\\\\\
\cfrac{dr}{dt}=\cfrac{y}{r}\cdot \cfrac{dy}{dt}$

so, what is "r" value 15 minutes later anyway?

$\bf r=\sqrt{(1500+4500+5400)^2+500^2}\implies r=\sqrt{11400^2+500^2}
\\\\\\
r=\sqrt{130210000}\implies r=100\sqrt{13021}$

then we just plug those folks in the derivative,

$\bf \cfrac{dr}{dt}=\cfrac{y}{r}\cdot \cfrac{dy}{dt}\qquad 
\begin{cases}
r=100\sqrt{13021}\\
\frac{dy}{dt}=11\\
y=11400
\end{cases}\implies \cfrac{dr}{dt}=\cfrac{11400}{100\sqrt{13021}}\cdot 11
\\\\\\
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3 years ago

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