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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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