Answered

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Which of the following would not be a possible function for f (x) and g(x) such that f of g of x is equal to 6 over the quantity x squared end quantity plus 3 f of x is equal to 6 over the quantity x squared end quantity plus 3 and g(x) = x f of x is equal to 6 over x plus 3 and g(x) = x2 f of x is equal to 6 over x plus 3 and g of x is equal to 1 over the quantity x squared end quantity f of x is equal to 2 over x plus 3 and g of x is equal to x squared over 3

Sagot :

The function that would not generate the desired composite function are:

[tex]f(x) = \frac{6}{x} + 3[/tex]

[tex]g(x) = \frac{1}{x^2}[/tex]

The composite function of f and g of x is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this problem, we want:

[tex]f(g(x)) = \frac{6}{x^2} + 3[/tex]

The first option is:

[tex]f(x) = \frac{6}{x^2}+3[/tex]

[tex]g(x) = x[/tex]

The composition is:

[tex]f(g(x)) = f(x) = \frac{6}{x^2}+3[/tex]

Which generates the desired function, thus, it is not the correct option.

The second option is:

[tex]f(x) = \frac{6}{x} + 3[/tex]

[tex]f(x) = x^2[/tex]

The composition is:

[tex]f(g(x)) = f(x^2) = \frac{6}{x^2}+3[/tex]

Which generates the desired function, thus, it is not the correct option.

The third option is:

[tex]f(x) = \frac{6}{x} + 3[/tex]

[tex]g(x) = \frac{1}{x^2}[/tex]

The composition is:

[tex]f(g(x)) = f(\frac{1}{x^2}) = \frac{6}{\frac{1}{x^2}}+3 = 6x^2 + 3[/tex]

Does not generate the desired function, so this is the correct option.

The fourth option is:

[tex]f(x) = \frac{2}{x} + 3[/tex]

[tex]g(x) = \frac{x^2}{3}[/tex]

The composition is:

[tex]f(g(x)) = f(\frac{x^2}{3}) = \frac{2}{\frac{x^2}{3}}+3 = \frac{6}{x^2}+3[/tex]

Which generates the desired function, thus, it is not the correct option.

A similar problem is given at https://brainly.com/question/23458455

Answer:

f of x is equal to 6 over x plus 3  and  g of x is equal to 1 over the quantity x squared end quantity

Step-by-step explanation:

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