Question

Consider the function g(x)= { (1/2)ˣ if x < 0

{ -x² if x > 0
Which statements are true about function g?

(a) g(x) is equal to (1/2)x when x<0.

(b) g(x) is equal to −x² when x>0.

(c) The function g(x) is defined at x=0.

(d) g(x) is decreasing for x<0.

Please select the correct options from the following:

a. (a) and (b)
b. (b) and (c)
c. (a) and (d)
d. (c) and (d)

Answer 1

The function g(x) is equal to -x^2 when x>0 and g(x) is decreasing for x<0. The other statements are false.

Step-by-step explanation:

The function g(x) is defined as:

g(x) = (1/2)^x if x < 0

g(x) = -x^2 if x > 0

1. (a) g(x) is equal to (1/2)x when x<0. This statement is false. The function g(x) is not equal to (1/2)x when x<0. It is equal to (1/2)^x.
2. (b) g(x) is equal to -x^2 when x>0. This statement is true. The function g(x) is equal to -x^2 when x>0.
3. (c) The function g(x) is defined at x=0. This statement is false. The function g(x) is not defined at x=0 because the function is not continuous at x=0.
4. (d) g(x) is decreasing for x<0. This statement is true. When x<0, the function g(x) = (1/2)^x, which is a decreasing function as x gets larger and more negative.