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ludmilkaskok [199]
4 years ago
9

The inverse of the function f(x)=

" title=" \sqrt{x + 3} + 2" alt=" \sqrt{x + 3} + 2" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
irina [24]4 years ago
3 0

Answer:

f^-1 (x)=x^2-4x+1

Step-by-step explanation:

y=sqrt(x+3)+2

x=sqrt(y+3)+2

sqrt(y+3)=x-2

y+3=(x-2)^2

y+3=(x-2)(x-2)

y+3=x^2-2x-2x+4

y+3=x^2-4x+4

y=x^2-4x+4-3

y=x^2-4x+1

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3x+12-15=10, 3x-3=10 what property is that
Softa [21]

Answer: subtraction property equality.

Step-by-step explanation:

8 0
3 years ago
Which of the following is equivalent to log408 rounded to three decimal places?
il63 [147K]

The answer is: 0.564

The explanation is shown below:

1. To solve this problem you must apply the following proccedure:

2. You have the logarithm expression:

log40(8)=x

3. First, you must apply the following property:

a^{loga(x)} =x

4. Therefore, you have:

40^{log40(8)}=40^{x} \\ 8=40^{x}

5. By applying logarithm on both sides, you have:

log(8)=log(40^{x} )

6. By applying the property log(a)^{b} =blog(a):

log(8)=xlog(40)

7. Solve for x:

x=log(8)/log(40)\\ x=0.564

4 0
3 years ago
If (3-4i) (x+iy) = 3 root 5<br> show that x^2 + y^2=9/5
NNADVOKAT [17]

Answer:

the answer is 2 + i.

Step-by-step explanation:

Let the square root of 3 + 4i be x + iy.

So (x + iy) (x +iy) = 3 +4i

=> x^2 + xyi + xyi + i^2*y^2 = 3 + 4i

=> x^2 – y^2 + 2xyi = 3 + 4i

Equate the real and complex terms

=> x^2 - y^2 = 3 and 2xy = 4

2xy = 4

=> xy = 2

=> x = 2/y

Substitute in

=> x^2 - y^2 = 3

=> 4/y^2 - y^2 = 3

=> 4 – y^4 = 3y^2

=> y^4 + 3y^2 – 4 = 0

=> y^4 + 4y^2 – y^2 – 4 =0

=> y^2(y^2 + 4) – 1(y^2 + 4) =0

=> (y^2 – 1) (y^2 + 4) =0

Therefore y^2 = 1, we ignore y^2 = -4 as it gives complex values of y.

Therefore y = 1 and x = 2/1 = 2

The required square root of 3 + 4i is 2 + i.

5 0
3 years ago
Multiply using distributive property: -5 ( 10 + 3y ) =
Jobisdone [24]

Answer:

-50 - 15y

Step-by-step explanation:

-5 ( 10 + 3y )

First distribute the -5 by multiplying it by 10 and 3y

(-5 x 10) + (-5 x 3y)

Than simplify

(-50) + (-15y)

Adding a negative is like subtracting a positive so you can turn (-50 + -15y) into (-50 - 15y)

Than you have your answer

-50 - 15y

5 0
4 years ago
There are 5280 feet in a mile and 12 inches in a foot. Explain how you can tell quickly if there are more or fewer than 50,000 i
siniylev [52]
Ten times 5280 is clearly more than fifty thousand. Since there are more than ten inches in one foot, we have even more than ten times 5289 inches in a mile, so there are many more than 50000 inches in one mile.
5 0
3 years ago
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