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just olya [345]
3 years ago
12

For what interval is the value of (f – g)(x) negative?

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
7 0

<u>Complete question:</u>

Refer the attached diagram

<u>Answer:</u>

In reference to the attached figure, (-∞, 2) is the value where (f-g) (x) negative.

<u>Step-by-step explanation:</u>

From the attached figure, it shows that given data:

f (x) = x – 3

g (x) = - 0.5 x

To Find: At what interval the value of (f-g) (x) negative

So, first we need to calculate the (f-g) (x)

(f – g ) (x) = f (x) – g (x) = x-3 - (- 0.5 x)

⇒ (f - g) (x) =1.5 x - 3

Now we are supposed to find the interval for which (f-g) (x) is negative.

⇒ (f - g) (x) = x - 3+ 0.5 x = 1.5 x – 3 < 0

⇒ 1.5 x – 3 < 0

⇒ 1.5 x < 3

⇒ x

⇒ x < 2

Thus for (f - g) (x) negative x must be less than 2. Thereby, the interval is (-∞, 2). Function is negative when graph line lies below the x - axis.

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