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3 years ago

F(x) = x2 - 4. Find the inverse of the function

Mathematics

1 answer:

Lisa [10]3 years ago

5 0

Answer:

$f^{-1}$ (x) = √ x + 4

Step-by-step explanation:

step 1) replace f(x) with y

y = x² - 4

step 2) switch the x and y (because every (x, y) has a (y, x))

x = y² - 4

step 3) add 4 to both sides of the equal sign

x + 4 = y²

step 4) take the square root of both sides of the equal sign (the square root symbol cancels out the ²)

√ x + 4 = y

step 5) you know have the inverse of f(x) = x² - 4

$f^{-1}$ (x) = √ x + 4

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Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.

This requires

$\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)$

$\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C$

So we have

$f(x,y)=-\cos x+\sin y+C$

which means $\vec F$ is indeed conservative. By the fundamental theorem, we have

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}$

3 0

3 years ago

A square coffee shop has sides that are 5 meters long. What is the coffee shop's area?

g100num [7]

Answer:

Step-by-step explanation:

If you want to find the area, you have to use this formula:

Formula:

LxW

L: length

W: Width

Here we have a square, and the sides are all 5 meters long, that means that we have to just do 5x5 to get the answer.

5x5=?

Hope ya remember the 5 table, lol, I know everyone does

5x5=25

so hence, your answer is 25m²

Thanks!

Answered by: FieryAnswererGT

#learnwithbrainly

8 0

3 years ago

Which two sets of events are most likely independent?

Bumek [7]

Answer:

A and C

Step-by-step explanation:

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.

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Options A and C are two sets of most likely independent events, because the girl's singing does not affect on her wish to become a lawyer and a man's hair doesn't depend on where his father lives.

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3 years ago

I need help in this question please help me!:)

anastassius [24]

Answer:

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Step-by-step explanation:

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melamori03 [73]

Answer:

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Step-by-step explanation:

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