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2 years ago

Identify the inverse g(x) of the given relation f(x).f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)}

Mathematics

2 answers:

laiz [17]2 years ago

5 0

F(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}
f(x) = ¹/₂x - 1

f(x) = ¹/₂x - 1
  y = ¹/₂x - 1
  x = ¹/₂y - 1
+ 1 + 1
  x + 1 = ¹/₂y
  2(x + 1) = 2(¹/₂y)
2(x) + 2(1) = y
2x + 2 = y
2x + 2 = f⁻¹(x)
2x + 2 = g(x)

g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}
g(x) = 2x + 2

Over [174]2 years ago

3 0

correct answer is g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

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2 years ago

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Answer:

For this case, the first thing we must do is define variables:

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10x + 6y <= 120

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Step-by-step explanation:

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2 years ago

A County Superintendent of Highways is interested in the numbers of different types of vehicles that regularly travel within his

Karolina [17]

Answer:

a) The ratio of passenger cars to pickup trucks is $\frac{5}{7}$

The ratio of pickup trucks to passenger cars is $\frac{7}{5}$

The ratio of passenger cars to total vehicles is $\frac{5}{12}$

The ratio of pickup trucks to total vehicles is $\frac{7}{12}$

b) The tape diagram is shown in the attached picture.

c) The tape diagram has 12 equal-sized parts.

d) The total quantity that the tape diagram represent is 192.

e) The value of each individual part of the tape is 16.

f) There were registered 80 passenger cars and 112 pickup trucks.

Step-by-step explanation:

a) According to the information in the problem, that for every 5 passenger cars registered, there were 7 pickup trucks registered.

So the ratios are:

Passenger cars to pickup trucks: $\frac{5}{7}$

Pickup trucks to passenger cars: $\frac{7}{5}$

If we calculate the total vehicles: 5+7=12

So, we can get two ratios more:

Passenger cars to total vehicles is $\frac{5}{12}$

Pickup trucks to total vehicles is $\frac{7}{12}$

b) We make a tape diagram where each box represents a vehicle so we draw 5 boxes for cars and 7 boxes for pickup trucks.

c) If we count the total quantity of boxes, there are 12.

d) This diagram represents the total quantity of registrations in August which is 192.

e) To get the representation of each part of the tape diagram we have to divide 192 by 12. 192÷12=16

f) Finally, we multiply 16 by the number of boxes of each type of vehicle:

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2 years ago

The starting salary for a particular job is 1.2 million per annum. The salary increases each year by 75000 to a maximum of 1.5mi

Vlada [557]

<h2>Answer:</h2>

In the 5th year

<h2>Step-by-step explanation:</h2>

For the first year, the salary is 1.2million = 1,200,000

For the second year, the salary is 1.2million + 75000 = 1,200,000 + 75,000 = 1,275,000

For the last year, the salary is 1.5million = 1,500,000

This gives the following sequence...

1,200,000 1,275,000 . . . 1,500,000

This follows an arithmetic progression with an increment of 75,000.

<em>Remember that,</em>

The last term, L, of an arithmetic progression is given by;

L = a + (n - 1)d ---------------(i)

<em>Where;</em>

a = first term of the sequence

n = number of terms in the sequence (which is the number of years)

d = the common difference or increment of the sequence

<em>From the given sequence,</em>

a = 1,200,000 [which is the first salary]

d = 75,000 [which is the increment in salary]

L = 1,500,000 [which is the maximum salary]

<em>Substitute these values into equation (i) as follows;</em>

1,500,000 = 1,200,00 + (n - 1) 75,000

1,500,000 - 1,200,000 = 75,000(n-1)

300,000 = 75,000(n - 1)

$\frac{300,000}{75,000} = n - 1$

4 = n - 1

n = 5

Therefore, in the 5th year the maximum salary will be reached.

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2 years ago

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Answer:

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So, our function will be:

P(t) = 27000 * (1-8/9)^(t/4)

P(t) = 27000 * (1/9)^(t/4)

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2 years ago

Read 2 more answers