Let ƒ(x) = 5x2 – x + 1 and g(x) = –3x. Evaluate the composition (ƒ ∘ g)(1) .

D

Step-by-step explanation:

We are given the two functions:

And we want to find:

Recall that this is equivalent to:

Evaluate g(1):

Substitute:

Evaluate f(-3):

Therefore:

Our answer is D.

  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).