Question

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

y= (2/x^2)+3

Answer 1

There are multiple solutions.

Answer 2

put \(g(x)=x^2+3\)

\[f(g(x))=\frac{2}{x^2+3}=\frac{2}{g(x)}\]
replace \(g(x)\) by \(x\), and you'll get \(f(x)\)

Answer 3

y= (2/x^2)+3 i meant

Answer 4

ooh.

put \(g(x)=x^2\)

Answer 5

\[f\big(g(x)\big)=\frac{2}{x^2}+3=\frac{2}{g(x)}+3\]
replace \(g(x)\) by \(x\)

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