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nadezda [96]
2 years ago
12

Given f of x is equal to the quantity x minus 4 end quantity divided by the quantity x squared plus 13x plus 36 end quantity, wh

ich of the following is true?
f(x) is decreasing for all x > –9
f(x) is increasing for all x < –9
f(x) is increasing for all x > –4
f(x) is decreasing for all x > –4
Mathematics
1 answer:
gavmur [86]2 years ago
8 0

The simplified expression of the function f(x) =\dfrac{x-4}{x^2+13x+36} is

f(x) = \dfrac{x-4}{(x+9)(x+4)}. f(x) is increasing for all x > –4.The correct answer is option C.

<h3>What is a function?</h3>

A function is defined as a relation between the set of inputs having exactly one output each.

The function expression is given as:

f(x) =\dfrac{x-4}{x^2+13x+36}

Expand the denominator

f(x) =\dfrac{x-4}{x^2+4x +9x+36}

Factorize the denominator

f(x) =\dfrac{x-4}{x(x+4)+9(x+4)}

Factor out x + 9

f(x) = \dfrac{x-4}{(x+9)(x+4)}

The simplified expression of the function f(x) =\dfrac{x-4}{x^2+13x+36} is

f(x) = \dfrac{x-4}{(x+9)(x+4)}. f(x) is increasing for all x > –4

Read more about functions at:

brainly.com/question/1851758

#SPJ1

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Step-by-step explanation:

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Given:

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b.

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