Question

Use the tables of ordered pairs to determine the value of each composite function. g(x) = √x f(x) = x² - 15 X 1 2 3 4 5 6 7 f(x) -14 -11 -6 1 10 21 34 X 1 4 9 16 25 36 49 g(x) 1 2 3 4 5 6 7 19] (fog)(36) = 20] (gog)(16) = 21] (gof)(4) = 22] (fof)(4) =​

Answer 1

To find the values of the composite functions, we use the tables provided to first evaluate the inner function and then the outer function, resulting in (fog)(36) = 21, (gog)(16) = 2, (gof)(4) = 1, and (fof)(4) = -14.

Step-by-step explanation:

Composite Functions

To determine the value of each composite function using tables of ordered pairs for the functions g(x) = √x and f(x) = x² - 15, we follow a step-by-step process of substitution:

(fog)(36): To find this, we look at the value of g(36), which is 6 according to the table. We then find f(6), which is 21. Thus, (fog)(36) = 21.

(gog)(16): We look up g(16), which yields 4. Then, we check g(4) and get 2. So, (gog)(16) = 2.

(gof)(4): For this, we evaluate f(4) finding 1, then apply g(1) and get 1. Hence, (gof)(4) = 1.

(fof)(4): We start with f(4), which is 1, then we find f(1) from the table, and we get -14. Therefore, (fof)(4) = -14.