Two functions are represented below. which function has a domain that contains the domain of the other function as a

subset?

f(x) = -log(x-2)-3

the function

has a domain that contains the domain as a subset of the function

Step-by-step explanation:

The domain of a function contains all possible values that it can take.

We can analyze the function:

[1]

And we can see that there are three functions in [1]:

and , and

or .

This operation is called function composition.

For every x, function h(x) can take any value, so the domain (all possible values this function can take) is (all real numbers).

However, function g(x) is restricted to positive values only, since log function is not defined for negative numbers and 0.

Therefore, domain for f(x) are restricted to those ones that comply with the above restriction (x > 0). So, for

Possible values are those which:

or

In words, the domain of f(x) are all values greater than 2 (but not equal to 2) or all positive real values greater than 2.

Then, the function f(x) has a domain that is a subset of function h(x), that is, in function h(x) = x - 2, x can takes any possible value from -(infinity) to infinity, whereas function f(x) can only takes those values greater than two (but not equal 2) to infinity, which makes the domain of f(x)  a subset of the possible values of function h(x).

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°