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defon
2 years ago
6

Simplify the function f(x)= 1/2 (27) 2x/3. Then determine the key aspects of the function

Mathematics
2 answers:
Andru [333]2 years ago
8 0

Answer:

The last one is y>0

jeyben [28]2 years ago
4 0
The given expression is:

f(x)= \frac{1}{2}(27)^{ \frac{2x}{3} } \\  \\ 
f(x)= \frac{1}{2}((27)^{ \frac{2}{3} })^{x}      \\  \\ 
f(x)=  \frac{1}{2}(9)^{x}

From the above equation, we can answer all the 4 questions.

a) Initial value occurs when x = 0

So,

f(0)= \frac{1}{2}(9)^{0}= \frac{1}{2}

So, the Initial value of the function is 1/2.

b) Simplified Base:
The base of an exponential function is the term which contains the exponent.
From the simplified equation, we can see that the base has been simplified and is equal to 9.

So, the simplified base is 9

c) Domain:
From the equation we can see that there is no such value which makes the function undefined. So all reall numbers are included in the Domain.

So, Domain is Set of All real numbers. 
In Interval notation this can be expressed as: (-∞,∞)

d) Range:
Range is the set of all y values that a function can take. Since the graph is not shifted vertically up or down, the range will be the set of all real numbers greater than zero.

So, Range is equal to All real numbers greater than 0.
In Interval notation, this can be expressed as (0,∞)
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If the function f(x) has a domain of (g,h) and a range of (j,k), then what is the domain and range of g(x) = m(f(x)] + p?​
sertanlavr [38]

Answer:

Dom\{g(x)\} = Dom\{f(x)\} = (g, h).

Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)

Step-by-step explanation:

From Mathematics we remember that the domain of a functions corresponds to the set of values of the independent variable (x in this case) so that images exist and the range of a function is the set of images.

In this case, we know the domain and range of f(x) and we must find the domain and range of g(x).

Domain

The domain of g(x) is the domain of f(x). That is, Dom\{g(x)\} = Dom\{f(x)\} = (g, h).

Range

We have to define the bounds of the range of g(x), given that range f(x) is modified by streching and horizontal translation operations:

Lower bound (f(x) = j)

g(x) = m\cdot j +p

Upper bound (f(x) = k)

g(x) = m\cdot k +p

In consequence, the range of g(x) is Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)

3 0
3 years ago
N times 2+1 equals what need help for 35 points
kupik [55]

Answer:

6846

Step-by-step explanation:


3 0
2 years ago
What is the approximate length of arc 9.9,19.9,21.5,43
Nataly_w [17]
I think the answer is 19.9 cm
4 0
2 years ago
Which is the inverse of the function y = 3(x − 4)?
koban [17]

Answer:

the answer is (1/3)x + 4 which is A. Give me brainlies

8 0
3 years ago
The thickness of each type of coin is shown in the table. How much thicker is stack of dollars worth of nickels than a dollars w
Lilit [14]
Let our basis be worth 1 dollar. A nickel's worth is $0.05. In order to come up with $1, the number of nickels should be:

Number of nickels = $1 * 1 nickel/$0.05 = 20 nickels
Thickness of 20 nickels = 20 nickels * 1.95 mm = 39 mm

Let's do the same for the quarters. Each quarter is worth $0.25.

Number of quarters = $1 * 1 quarter/$0.25 = 4 quarters
Thickness of 4 quarters = 4 quarters * 1.75 mm = 7 mm

Find the ratio of the two:
39 mm/7 mm = 5.57

Therefore, a stack of nickels is 5.57 times thicker than a stack of quarters worth one dollar.
7 0
3 years ago
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