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2 years ago

Let f(x) =2x and g(x)= x - 2 the graph of (f.g )(x) is shown below

Mathematics

1 answer:

Vika [28.1K]2 years ago

6 0

Answer:

The domain of the graph is all real number ⇒ the last answer

Step-by-step explanation:

* Remember that our original exponential formula was y = ab^x

- The b value is the growth factor

* Lets revise how to find the domain of this function

- The domain is all values of x that make the function defined

* Lets revise the composite function

- A composite function is a function that depends on another function.

- A composite function is created when one function is substituted

into another function.

- For example, f(g(x)) is the composite function that is formed when

g(x) is substituted for x in f(x).

∵ f(x) = 2^x

∵ g(x) = x - 2

∴ (f · g)(x) = f(x - 2)

∵ f(x) = 2^x

∴ (f · g)(x) = f(x - 2) = 2^(x - 2)

- For this function there is no values of x make the function undefined

∴ The Domain is all real numbers

- Look to the graph, the values of x go from -∞ to ∞

* The domain of the graph is all real number

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Convert this rational number to its decimal form and found to the nearest thousands?

pentagon [3]

Answer:

7 and 1 respectively

Step-by-step explanation:

1/7= 7 ) 1 (, the basic definition of division

7 0

3 years ago

If your starting salary were $50,000 and you received a 4% increase at the end of every year for 15 years, what would be the tot

ycow [4]

Answer-

The total amount you would have earned over the first 16 years is $90047.20

Solution-

The exponential function that would given the growth is,

$P'=P(1+r)^t$

Where,

P' = Future value,

P = Current value = $50000

r = rate of change = 4% = 0.04

t = time = 15 year (not 16 because the the increment occurs at year end and we want to get the value at the beginning of 16th year)

Putting the values,

$P'=50000(1+0.04)^{15}$

$=50000(1.04)^{15}$

$=90047.20$

Therefore, the total amount you would have earned over the first 16 years is $90047.20

6 0

3 years ago

Read 2 more answers

What are the mean, median, mode, and range of the data set given the altitude of lakes in feet: -11, -28, -17, -25, -28, -39, -6

GrogVix [38]

Answer:

Mean=-21.5

Median=-26.5

Mode=-28

Range= -6 to-46

Step-by-step explanation:

Arranging the numbers given either in ascending or descending order. In this case, I used descending order as follows

-6

-11

-17

-25

-28

-39

-46

Mode is the number that occurs more than others. In this case, only -28 appears twice hence it is the mode

The mean is given by adding all the numbers and dividing by the frequency.

The sum of numbers will be -6+-11+-17+-25+-28+-28+-39+-46=-172

Mean=-172/8=-21.5

The median is the number that appears in the middle after arranging the numbers in descending order as above. In this case, two numbers appear in the middle, that is -25 and -28 hence median -25+-28/2=-26.5

The range of numbers id from -6 to-46 as arranged above

8 0

2 years ago

whitney is training to ride her bicycle in a big race. The table below shows hiw many miles she rides each day of one week

hoa [83]

Answer: C (24.5 miles more)

Step-by-step explanation:

on Friday she rode 42.4 miles

on Tuesday she rode 17.9 miles

you just subtract Tuesday’s miles from Friday’s miles

42.4 - 17.9 = 24.5

so, C

7 0

3 years ago

Sam is renting one of two cars to go on a 300-mile trip. The first car can travel 75 miles on 5 gallons of gas. The second car c

Doss [256]

Solution:

The first car can travel 75 miles on 5 gallons of gas.

So per mile gas consumed by car $=\frac{5}{75}=\frac{1}{15}$ gallon

The second car can travel 240 miles on 20 gallons of gas.

So per mile gas consumed by car $=\frac{20}{240}=\frac{1}{12}$ gallon

It mean Sam should rent the First car.

Sam is renting one of two cars to go on a 300-mile trip.

So total number of gallons of gas required $=\frac{1}{15}*300=20$

Total cost of 20 gallons of gas $=\frac{49.42}{14}*20= 70.6$ dollar

3 0

2 years ago