Answer to Question #330654 in Algebra for Ashish

Question

Express the function g ,defined by g(x)=1/√x+√x,as a composition of three function

Answer 1

$f(x)=\sqrt{x},\;g(x)=\sqrt{x^2+x},\;h(x)=\frac{1}{x}.$

$g(f(x))=\sqrt{(\sqrt{x})^2+\sqrt{x}}=\sqrt{x^2+x}.$

$h(g(f(x)))=\frac{1}{g(f(x))}=\frac{1}{\sqrt{x^2+x}}.$