Question

Evaluate the function at the given values of the independent variable. Simplify the results.

g(x) = x2(x − 2)
(a) g(2)
(b) g 3 2
(c) g(c)
(d) g(t + 2)

Answer 1

To evaluate the function g(x) = x2(x − 2) at different values of the independent variable, we substitute the values into the function and simplify. g(2) = 0, g(3/2) = -9/8, g(c) = c3 − 2c2, and g(t + 2) = t3 + 4t2 + 4t.

Step-by-step explanation:

To evaluate the function g(x) = x2(x − 2), we substitute the given values of the independent variable (x) into the function and simplify the results.

(a) g(2) = 22(2 − 2) = 22(0) = 0

(b) g(3/2) = (3/2)2((3/2) − 2) = (3/2)2(-1/2) = 9/4 * -1/2 = -9/8

(c) g(c) = c2(c − 2) = c3 − 2c2

(d) g(t + 2) = (t + 2)2((t + 2) − 2) = (t + 2)2(t) = t3 + 4t2 + 4t