Find f(x), ifg(x)=1+x and f[g(x)]=3+2 x+x. - Vidyadip

Question

Find $f(x)$,
if$g(x)=1+\sqrt{x}$ and $f[g(x)]=3+2 \sqrt{x}+x$.

✓

Answer

$ g(x)=1+\sqrt{x}$
$f(g(x))=3+2 \sqrt{x}+x$
$=x+2 \sqrt{ } x+1+2$
$=(\sqrt{ } x+1)^2+2$
$f(\sqrt{ } x+1)=(\sqrt{ } x+1)^2+2$
$\therefore f(x)=x^2+2 $

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