What is the inverse of f(x) = (x+6)² for x ≥ -6 where function g is the inverse of function f?
a. g(x) = x+6√, x≥−6
b. g(x) = x−6√, x≥6
c. g(x) = x√−6, x≥0
d. g(x) = x√+6, x≥0

Step-by-step explanation:

We have f(x) = (x+6)² for x ≥ -6

That is

             y = (x+6)²

We know that negative of square root value is not defined.

So x should be greater than or equal to zero.

So

Option C is the correct answer.

  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).

answer: h

step-by-step explanation: