Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)).

y = Two divided by x squared. + 3

Answer 1

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

Answer 2

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) =$\frac{2}{x+3}$