Question

Find the function value, if possible. (If an answer is undefined, enter UNDEFINED.)

g(t) = 7t^2 − 6t + 5
(a) g(2)
(b) g(t − 2)
(c) g(t) − g(2)

Answer 1

To find function values, substitute the given values of t into the function g(t). Evaluating each part, we get g(2) = 21, g(t - 2) = 7t^2 - 34t + 45, and g(t) - g(2) = 7t^2 - 6t - 6.

Step-by-step explanation:

To find the function values, we substitute the given values of t into the function g(t). Let's evaluate each part:

(a) g(2) = 7(2)^2 - 6(2) + 5 = 7(4) - 12 + 5 = 28 - 12 + 5 = 21

(b) g(t - 2) = 7(t - 2)^2 - 6(t - 2) + 5 = 7(t^2 - 4t + 4) - 6(t - 2) + 5 = 7t^2 - 28t + 28 - 6t + 12 + 5 = 7t^2 - 34t + 45

(c) g(t) - g(2) = (7t^2 - 6t + 5) - (7(2)^2 - 6(2) + 5) = 7t^2 - 6t + 5 - 28 + 12 + 5 = 7t^2 - 6t - 6