For this case we have the following functions:
[tex]f (x) = 3-2x\\g (x) = \frac {1} {x + 5}[/tex]
We must find:[tex]\frac {f} {g} (8)[/tex]
By definition we have to:
[tex]\frac {f} {g} (x) = \frac {f (x)} {g (x)}[/tex]
So:
[tex]\frac {f (x)} {g (x)} = \frac {3-2x} {\frac {1} {x + 5}} = (3-2x) (x + 5)[/tex]
Thus, we have to:
[tex]\frac {f} {g} (8) = (3-2 (8)) (8 + 5) = (3-16) (13) = - 13 * 13 = -169[/tex]
So, the value is -169
ANswer:
Option A
The value of function [tex]\dfrac{f}{g}(8)[/tex] is given by: Option A: -169
Suppose the considered functions are [tex]f(x)[/tex] and [tex]g(x)[/tex]
Then, we get a new function as ratio of these two functions as:
[tex]h(x) = \dfrac{f}{g}(x) = \dfrac{f(x)}{g(x)}[/tex] (defined for all x such that g(x) ≠ 0)
For this case, we are given:
Thus, we get:
[tex]\dfrac{f}{g}(x) = \dfrac{f(x)}{g(x)} = f(x) \times \dfrac{1}{g(x)} = (3-2x)\dfrac{1}{1/(x+5)}\\\\\dfrac{f}{g}(x) = (3-2x)(x+5)[/tex]
At x = 8, we get:
[tex]\dfrac{f}{g}(x) = (3-2x)(x+5)\\\\\dfrac{f}{g}(8) = (3-2(8))(8+5) = -13 \times 13 = -169[/tex]
Thus, the value of [tex]\dfrac{f}{g}(8)[/tex] is given by: Option A: -169
Learn more about composite functions here:
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