Consider the function f(x)=9-x^2/x^2-4 for which intervals is f(x) positive? check all that apply.

a. (-infinity, -3)

b. (-3, -2)

c. (-2, 2)

d. (2, 3)

e. (infinity, 3)

(brainliest will be awarded, rated, and )

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:

a. (-infinity, -3)

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,∞)

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d

step-by-step explanation: