Determine the domain of the function. f as a function of x is equal to the square root of x plus three divided by x plus eight times x minus two. All real numbers except -8, -3, and 2
x ≥ 0
All real numbers
x ≥ -3, x ≠ 2

Step-by-step explanation:

The function is given,

The domain of a function are all possible values of x.

There are restrictions for the value of x.

The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.

Subtract 8 from both parts.

Add 2 on both parts.

The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.

Subtract 3 from both parts.

The domain of the function is , .

  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).

4.08%

step-by-step explanation: