2. justify each step of the proof.
conjecture: if 2(x2 + 5) = 60, then x is 5 or –5.
1. 2(x2 + 5) = 60 1.
2. 2x2 + 10 = 60 2.
3. 2x2 = 50 3.
4. x2 = 25 4.
5. x = ±5 5.

:

step-by-step explanation:

  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).