Question

If f(x)=3x+5,g(x)=6x-1,then find (f/g)(x) and it's domain​

Answer 1

Refer to the attachment

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Answer 2

$\big(\dfrac{f}{g}\big)(x) = \dfrac{3x+5}{6x-1}$

Domain: $(-\infty,\dfrac{1}{6})\cup (\dfrac{1}{6},\infty)$

Step-by-step explanation:

We are given the following in the question:

$f(x) = 3x+5\\g(x) = 6x-1$

We have to find

$\big(\dfrac{f}{g}\big)(x)$  

$= \dfrac{f(x)}{g(x)} = \dfrac{3x+5}{6x-1}$

We define domain of a function are all the possible values of x for which the function is defined.

Thus, the domain of

$\big(\dfrac{f}{g}\big)(x)$

The singular point for given function is

$6x -1 = 0\\\\x = \dfrac{1}{6}$

Thus, the domain is:

$(-\infty,\dfrac{1}{6})\cup (\dfrac{1}{6},\infty)$

#Learnmore:

If f(x) = x2 – 25 and g(x) = x – 5 what is the domain of (f/g)(x)

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