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vagabundo [1.1K]
3 years ago
14

Find the inverse of the function. y = x2 + 4x + 4

Mathematics
2 answers:
alex41 [277]3 years ago
7 0
<span>The given function is ⇒⇒⇒  y = x² + 4x + 4
</span>
To find the inverse of the function, we need to make x as a function of y and at the final step make a switch between x and y (i.e. make x as y and y as x)
y = x² + 4x + 4  ⇒⇒⇒ factor the quadratic equation
y = (x+2)(x+2)
y = (x+2)²         ⇒⇒⇒ take the square root to both sides
√y = x+2
x = √y - 2         ⇒⇒⇒ x becomes a function of y
final step:
∴ y = √x - 2   ⇒⇒⇒ the inverse of the given function

So, as a conclusion:
f(x) = y = x² + 4x + 4  ⇒⇒⇒ the given function

f⁻¹(x) = y = √x - 2       ⇒⇒⇒ the inverse of the given function


Sever21 [200]3 years ago
3 0

The answer is the third one

y=+-√x-2

Hopes this helps, and God bless <3

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an ivy plant was 19 inches long. two years later it was 33 inches long. what was the percent increase to the nearest hundredth o
lapo4ka [179]

Answer:

73.68%

Step-by-step explanation:

To find the amount of increase subtract 33-19 to get 14.

The percent increase is the amount of increase/initial length * 100

So 14/19*100 = 73.684...

Rounding to the nearest hundredth = 73.68%

4 0
3 years ago
1/x^-2 x=7 yeet yeet
Yanka [14]

Answer:

49

Step-by-step explanation:

x = 7

1 / x^-2

= x^2

= 7^2

= 49

8 0
3 years ago
Solve for x on the interval [0, 2pi]<br> Sinx = cosx + 1
lisov135 [29]

Answer:

π

Step-by-step explanation:

Solve for x on the interval [0, 2pi]

Given the equation

Sinx = cosx + 1

Square both sides of the equation

Sin²x = (cos x + 1)²

Sin²x = cos²x + 2cos x + 1

Since Sin²x = 1 - cos²x

1 - cos²x = cos²x + 2cos x + 1

Collect like terms

1-1-cos²x-cos²x-2cos x  = 0

-2cos²x-2cos x = 0

-2cos²x = 2cos x

-cosx = 1

cos x = -1

x = arccos -1

x = 180 degrees

<em>Hence the value of x = π</em>

8 0
3 years ago
On January 1, 2010, Joline deposits $1000 in a bank account that does not earn interest. For the next 12 months she deposits $25
hjlf

Answer:

$1000 + $25m and $1300 - 25m ;

1100 + 2.75m

2010 (4th month)

2011 ( 7th month)

Step-by-step explanation:

Joline's account :

Initial deposit = $1000

Monthly deposit = $25

Monthly withdrawal = $25

Number of months = 12

Let m = number of month at any point in time

Initial deposit + total deposit

Amount in Joline's account ; first 12 months

$1000 + $25m - - - (1)

Next 12 months :

$1000 + $25 *12 - 25m

1300 - 25m

Sofia's account :

Deposit amount = $1100

Interest per month = 0.25% = 0.0025

1100 + (1100 * 0.0025 * m)

1100 + 2.75m - - (2)

To find the month:

Equate equation 1 and 2, then find m

$1000 + $25m = 1100 + (1100*0.0025*m)

1000 + 25m = 1100 + 2.75m

25m - 2.75m = 1100 - 1000

22.25m = 100

m = 100 / 22.25

m = 4.494

In year 2010, they have approximately the same amount in the fourth month

1300 - 25m = 1100 + 2.75m

1300 - 1100 = 2.75m + 25m

200 = 27.75m

m = 200 / 27.75

m = 7.207

In 2011 ; they have approximately the se amount in the 7th month

4 0
3 years ago
Kasian needs to figure the amount of paint for a circle 14 feet in diameter what is the area of the circle he is painting
dolphi86 [110]
49π (153.938) is the area of the circle. 
Formula is πr²
π(7)²
49π
5 0
3 years ago
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