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pochemuha
3 years ago
6

1) Find the inverse function of f(x)=1/2x+3

Mathematics
2 answers:
dexar [7]3 years ago
8 0
 y = 1/2x + 3
change x and y

x = 1/2y + 3
now find the value of y and that is inverse function 

x - 3 =1/2 y
y = 2x- 6
 
f-(x) = 2x - 6
<u />

for both domain : ( - ∞ , + ∞ )

range f (x) : ( - ∞ , + ∞ )  - { 0 }
range f-(x) :( -∞ , +∞)
Gre4nikov [31]3 years ago
5 0
To find the inverse function you need to change f(x) (call it y) and x, then solve for y:

y = \frac{1}{2}x+3 \\ x = \frac{1}{2}y + 3 \\ x - 3 = \frac{1}{2}y \\ 2x-6 = y

So now you have f^{-1}(x) = 2x-6.

Composition to prove inverse relation: f \circ f^{-1} (x) = x:

f(f^{-1}(x)) = \frac{1}{2}(2x-6)+3 = x - 3 + 3 = x \square

Domain and Range of both functions is Real numbers since they are both linear equations.
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In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-sevent
Otrada [13]

Answer:

60 ships.

Step-by-step explanation:

Let the total number of ships in the naval fleet be represented by x

One-third of the fleet was captured = 1/3x

One-sixth was sunk = 1/6x

Two ships were destroyed by fire = 2

Let surviving ships be represented by y

One-seventh of the surviving ships were lost in a storm after the battle = 1/7y

Finally, the twenty-four remaining ships sailed home

The 24 remaining ships that sailed home =

y - 1/7y = 6/7y of the surviving fleet sailed home.

Hence

24 = 6/7y

24 = 6y/7

24 × 7/ 6

y = 168/6

y = 28

Therefore, total number of ships that survived is 28.

Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4

Total number of ships in the fleet(x) =

x = 1/3x + 1/6x + 2 + 28

Collect like terms

x - (1/3x + 1/6x) = 30

x - (1/2x) = 30

1/2x = 30

x = 30 ÷ 1/2

x = 30 × 2

x = 60

Therefore, ships that were in the fleet before the engagement were 60 ships.

3 0
2 years ago
What is the slope of y-4=5/2(x-2)
OLEGan [10]
The answer is 5/2. The equation is already in point slope form. If you recall, the equation for point slope form is y-y1 = m(x-x1) where y1 and x1 are points on the graph, and m is the slope. In the given equation, m is 5/2 so we know it is the slope.
Alternatively, if you are not familiar with the point slope for equation, you can manipulate the equation to the form of y=mx+b where m is the slope and b is the constant. If you solve for y, you get y=5/2x-1 since 5/2 is in the place of m, we know 5/2 is the slope.

6 0
3 years ago
Find the area of this circle. Use 3.14 for pi
aalyn [17]
The area of a circle is given by the formula:

A = \pir^2

Since \pi = 3.14, and r = 6, sub these values into the equation,

A = 3.14 x 6^2
   = 113.04

Hope this helped!
8 0
3 years ago
What has the same value as 65% of 20
snow_tiger [21]

Answer:

13

Step-by-step explanation:

We want to find 65% of 20

65% *20

Changing to decimal form

.65 *20

13

6 0
3 years ago
Read 2 more answers
2 + 2= ?<br><br> Just answer this if ur bored
Galina-37 [17]

Answer:

4

Step-by-step explanation:

break the first 2 into its components, 1 and 1 because 1 + 1 = 2.
Break the second 2 into its components, 1 and 1 because 1 + 1 = 2.

Combine all the components. Since they're all ones, you just have to count your fingers 4 times!
1 + 1 = 2. 2 + 1 = 3. 3 + 1 = 4!
1 + 1 + 1 + 1 = 4!

4 is the correct answer.

5 0
2 years ago
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