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Verified Answer :

Nirina7

y=2/x² +3
let's find f and g
y=f(g(x))=2/x² +3,        y-3= 2/x² , so f^-1(y)= y-3= 2/x² = g(x)
so g(x) =2/x²
but y = 2/x² +3, so y= g(x)+3= f(g(x)), consequently, f(x) = x+3

finally f(x) = x+3, and g(x)=2/x²





JeanaShupp

Answer: g(x) =\(x^2\)

and f(x) =\(\frac{2}{x+3}\)


Step-by-step explanation:

\(y=\frac{2}{x^2+3}\)

To find f(x) and g(x) such that

\(y=f(g(x))=\frac{2}{x^2+3}\),     

Then only one possible answer is g(x) =\(x^2\)

and f(x) =\(\frac{2}{x+3}\) such that

\(\text{the composite function will be }\ f(g(x))=f(x^2)=\frac{2}{(x^2)+3}=\frac{2}{x^2+3}\)

Thus, g(x) =\(x^2\)

and f(x) =\(\frac{2}{x+3}\)

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