Question

Given f (x)= x-4/x^2+13x+36, which 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

Answer 1

The simplified expression of the function [tex]f (x)= \frac{x-4}{x^2+13x+36}[/tex] is

[tex]f (x)= \frac{x-4}{(x+9)(x+4)}[/tex]. f(x) is increasing for all x > –4

What is a function?

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

The function expression is given as:

[tex]f (x)= \frac{x-4}{x^2+13x+36}[/tex]

Expand the denominator

[tex]f (x)= \frac{x-4}{x^2+4x+9x+36}[/tex]

Factorize the denominator

[tex]f (x)= \frac{x-4}{x(x+4)+9(x+4)}[/tex]

Factor out x + 9

[tex]f (x)= \frac{x-4}{(x+9)(x+4)}[/tex]

Hence, the simplified expression of the function [tex]f (x)= \frac{x-4}{x^2+13x+36}[/tex] is

[tex]f (x)= \frac{x-4}{(x+9)(x+4)}[/tex]. f(x) is increasing for all x > –4

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