Answer :

aklee18oo

Answer:

B

Step-by-step explanation:

To find [tex](\frac{f}{g} )(x)[/tex] you can write the expression as [tex]\frac{f(x)}{g(x)}[/tex]. We can substitute the f(x) and g(x) into the expression to get: [tex]\frac{\sqrt[3]{4x} }{2x+3}[/tex]. Now we need to find the domain. The numerator is fine, and the domain is all real numbers, but in a fraction, the denominator cannot equal 0. We can write:  [tex]2x + 3\neq 0[/tex] and we can solve it:

[tex]2x\neq -3[/tex]

[tex]x\neq -\frac{3}{2}[/tex]

This is the same as option B.

abidemiokin

The required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2. Option C is correct

Given the functions

f(x) = 3√4x

g(x) = 2x + 3

We are to find the resulting function (f/g)(x)

(f/g)(x) = f(x)/g(x)

(f/g)(x) = 3√4x/2x+3

Restriction to the function occurs at the point where the denominator is zero.

2x = 3 = 0

2x = -3

x = -3/2

Hence the required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2

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