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4 years ago

Given f(x) = V6x and g(x) =

Mathematics

1 answer:

AURORKA [14]4 years ago

4 0

Answer:

8 is the only one that will work

Step-by-step explanation:

(f o g)(x)=f(g(x)).

So this means the x will first be plug into g.

So let's check your choices.

g(6)=1/(6-6)=1/0 so 6 is not in the domain of g which means it isn't in the domain of (f o g).

g(8)=1/(8-6)=1/2 so this is a number so 8 is in the domain of g,

Let's check if 1/2 is in the domain of f.

f(1/2)=sqrt(6*1/2)=sqrt(3) so this is a number so since 1/2 is in the domain of f then 8 is in the domain of (f o g).

g(4)=1/(4-6)=1/(-2)=-1/2 so 4 is in the domain of g,

f(-1/2)=sqrt(6*-1/2)=sqrt(-3) so this is a problem because you can't square root negative numbers so -1/2 isn't in the domain of f, and therefore 4 isn't in the domain of (f o g).

g(2)=1/(2-6)=1/-4=-1/4 so 2 is in the domain of g.

f(-1/4)=sqrt(6*-1/4)=sqrt(-3/2) so again this is a problem because we can't square root negative numbers so -1/4 isn't in the domain of f, and therefore 2 isn't in the domain of (f o g).

You might be interested in

the sum of 2 numbers is 49. Twice the smaller number is 97 less than 3 times the larger number. What are the numbers?

ivanzaharov [21]

Answer:

let the larger and smaller number be x and y respectively

first condition

x + y = 49

second condition

3x = 2y+97

3x-2y =97

Multiplying first condition by two and adding both equations

2x + 2y = 98

5x = 195

x = 195/5 = 39

putting the value of x in

x + y = 49

y = 49 -39 = 10

again

Step-by-step explanation:

3 0

3 years ago

The value of savings account can be modeled by the function S(x) = 5, 000 * (1.025) ^ (0.7x) x is the number of years 1980. What

garik1379 [7]

Answer:

The approximate growth rate of the savings account is 2.5%

Step-by-step explanation:

Given the the function S(x) = 5, 000 * (1.025) ^ (0.7x)

From the function, we can see that part: (1.025). It presents for the growth factor or rate with the formula as:

(1 + r) where r is rate

So we have:

(1 + r) = 1.025

<=> r = 1.025 -1

<=> r = 0.025

In pecentage, we have the rare: 0.025 *100% = 2.5%

So the approximate growth rate of the savings account is 2.5%

8 0

4 years ago

The grade point averages (GPA) for 12 randomly selected college students are shown on the right. Complete parts (a) through (c)

Ilya [14]

Answer:

$\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29$

$s=1.09$

Step-by-step explanation:

For this case we have the following data given:

2.3 3.1 2.8

1.7 0.9 4.0

2.1 1.2 3.6

0.2 2.4 3.2

Since the data are assumedn normally distributed we can find the standard deviation with the following formula:

$\sigma =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}$

And we need to find the mean first with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And replacing we got:

$\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29$

And then we can calculate the deviation and we got:

$s=1.09$

7 0

3 years ago

Read 2 more answers

A certain television is advertised as a 53-inch TV (the diagonal length). If the width of

zhenek [66]

The TV is 45 inches tall.

Step-by-step explanation:

The diagonal length of television = 53 inches

Width of TV = 28 inches

As TV is in rectangular or square shape, a diagonal will form a right triangle

Where,

Diagonal = hypotenuse = c = 53 inches

Width = base = b = 28 inches

Length = perpendicular = a

we will use pythagorean theorem to find the length.

$a^2+b^2=c^2\\a^2+(28)^2=(53)^2\\a^2+784=2809\\a^2=2809-784\\a^2=2025$

Taking square root on both sides

$\sqrt{a^2}=\sqrt{2025}\\a=45$

The TV is 45 inches tall.

Keywords: triangle, square root

Learn more about square root at:

#LearnwithBrainly

6 0

4 years ago

Subtract 12x + 7 from 36 + 13

jeka94

Answer:

56-12x

Step-by-step explanation:

36+13-12x+7

49-12x+7

56-12x

5 0

3 years ago