Answer:
a. f (x) < 0 for x ∈ (-∞ ,-3)
b. f (x) > 0 for x ∈ (-3,-2)
c. f (x) < 0 for x ∈ (-2,2)
d. f (x) > 0 for x ∈ (2,3)
e.f (x) < 0 for x ∈ (3,∞)
Step-by-step explanation:
Here, the given function is:
Now, to check for the sign of f(x) at x = k, put the value of x from the given interval.
We get:
<u>a. (-infinity, -3) </u>
put k = -4 from the given interval
We get
⇒ f (x) < 0 for x ∈ (-∞ ,-3)
b. (-3, -2)
put k = -2.5 from the given interval
We get
⇒ f (x) > 0 for x ∈ (-3,-2)
c. (-2, 2)
put k = 0 from the given interval
We get
⇒ f (x) < 0 for x ∈ (-2,2)
d. (2, 3)
put k =2.5 from the given interval
We get
⇒ f (x) > 0 for x ∈ (2,3)
e. (infinity, 3)
put k = 4 from the given interval
We get
⇒ f (x) < 0 for x ∈ (3,∞)