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The function (fog)(x) is the composition of the functions f(x) and g(x). In this example, substituting g(x) into f(x) we obtain (fog)(x) = 2/(1/2x)+3, which simplifies to 4x/(1+6x).
The function (fog)(x) represents the composition of the functions f(x) and g(x). In this case, it implies putting the function g(x) inside the function f(x). To perform this operation, we need to replace x in the f(x) function with the g(x) function.
To facilitate understanding, let's go with an easy-to-use approach step by step to find (fog)(x).
So, (fog)(x) when f(x)=2/x+3 and g(x) = 1/2x is 4x/(1+6x).
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Rewritten by : Barada
Answer:
1st option
Step-by-step explanation:
To obtain (f ￮ g)(x) , substitute x = g(x) into f(x)
(f ￮ g)(x)
= f(g(x)
= f([tex]\frac{1}{2x}[/tex] )
= [tex]\frac{2}{\frac{1}{2x}+3 }[/tex]
= [tex]\frac{2}{\frac{1}{2x}+3 }[/tex] × [tex]\frac{2x}{2x}[/tex]
= [tex]\frac{4x}{1+6x}[/tex]
