Question

given f(x)=x+4/x2-3x-28 which of the following is true
-f(x) is positive for all x>-4
-f(x) is negative for all x>-4
-f(x) is positive for all x<7
-f(x) is negative for all x<7

Answer 1

Answer:

f(x) is negative for all x<7

Step-by-step explanation:

Factor denominator.

The denominator can be factored as follows:

−3x−28=(x−7)(x+4)

Rewrite the problem into:

f(x)= x+4/(x−7)(x+4)

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For x< − 4 x<−4: In this interval,  x−7 is negative, so f(x) is negative.

For − 4 < x < 7: In this interval, x−7 is negative, so f(x) is negative.

For x> 7: In this interval, x−7 is positive, so f(x) is positive.

Therefore, the correct statement is: f(x) is negative for all x<7