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3 years ago

Does anyone know what the inverse function of f(x)=x/x-2 is?

Mathematics

1 answer:

Leto [7]3 years ago

4 0

Answer:

-1 is the answer to that

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Solve the differential. This was in the 2016 VCE Specialist Maths Paper 1 and i'm a bit stuck

Nimfa-mama [501]

$\sqrt{2 - x^{2}} \cdot \frac{dy}{dx} = \frac{1}{2 - y}$
$\frac{dy}{dx} = \frac{1}{(2 - y)\sqrt{2 - x^{2}}}$

Now, isolate the variables, so you can integrate.
$(2 - y)dy = \frac{dx}{\sqrt{2 - x^{2}}}$
$\int (2 - y)\,dy = \int\frac{dx}{\sqrt{2 - x^{2}}}$
$2y - \frac{y^{2}}{2} = sin^{-1}\frac{x}{\sqrt{2}} + \frac{1}{2}C$

$4y - y^{2} = 2sin^{-1}\frac{x}{\sqrt{2}} + C$
$y^{2} - 4y = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} - 4 = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} = 4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C$

$y - 2 = \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$
$y = 2 \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$

At x = 1, y = 0.
$0 = 2 \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$
$-2 = \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C > 0$
$\therefore 2 = \sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 = 4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C$
$0 = -2sin^{-1}\frac{1}{\sqrt{2}} - C$
$C = -2sin^{-1}\frac{1}{\sqrt{2}} = -2\frac{\pi}{4}$
$C = -\frac{\pi}{2}$

$\therefore y = 2 - \sqrt{4 + \frac{\pi}{2} - 2sin^{-1}\frac{x}{\sqrt{2}}}$

6 0

3 years ago

A teacher asked four of her students to write an expression for the problem below. All products in a store are being discounted

Sunny_sXe [5.5K]

Answer:

she iduno

Step-by-step explanation:

8 0

3 years ago

Should you use Sine, Cosine, or Tangent to solve the following problem

olga55 [171]

tangent

Step-by-step explanation:

because it gave u an angel and and adjacent so your x is the opposite so sin20=x÷17 just use your calculator u will find the ans

8 0

3 years ago

The veterinarian told Hector that his 8-inch puppy would get no taller than 24 inches. Write and solve an inequality to find how

vladimir1956 [14]

Answer:

8<x>24

Step-by-step explanation:

It grow greater than 8 but less than 24.

If you're still not getting it ask me in the comments below.

Hope this helps

3 0

3 years ago

ABCD is a parallelogram angle a is equal to (5x-2) and angle c is equal to 48 find x

bulgar [2K]

For a parallelogram, we know that there are to pairs of angles that are the same and that all 4 angles add to 360.

2(5x-2)+2(48)=360
2(5x-2)+96=360
10x-4+96=360
10x+92=360
10x=268
x=26.8

Final answer: x=26.8

Hope this helps!

3 0

3 years ago