Question

let g(x) = x if x < 1 2 if x = 1 2 − x2 if 1 < x ≤ 2 x − 3 if x > 2 . (a) evaluate each of the following, if it exists. (if an answer does not exist, enter dne.)

Answer 1

To evaluate the given expressions, substitute the values of x into the function g(x) and simplify. Some expressions may not exist since the function is not defined for certain values of x.

Step-by-step explanation:

To evaluate each expression, we substitute the given values of x into the function g(x) and simplify.

a) g(1.5) = 2 - (1.5)^2 = 2 - 2.25 = -0.25

b) g(4.5) does not exist because the function is not defined for values of x greater than 2.

c) g(0.3333) = 0.3333 (since 0.3333 is less than 1)

d) g(0) does not exist because the function is not defined for values of x less than 1.

e) g(0.6) = 0.6 (since 0.6 is less than 1)

f) g(12) = 12 - 3 = 9

g) g(6) does not exist because the function is not defined for values of x greater than 2.

h) g(6) does not exist because the function is not defined for values of x greater than 2.