Answer to Question #108039 in Calculus for Anurag

Question

Express the function g:R_R. Defined by th g(x) as the composition of the three

Answer 1

$g(x)=\frac {1}{\sqrt{x+\sqrt{x}}},$ $g:R^+\to R^+$

Let $f(x)=\sqrt{x}$

$h(x)=\sqrt{x^2+x}$

$k(x)=\frac 1 x$

We find:

$h(f(x))=\sqrt{x+\sqrt{x}}$

Again:

$k(h(f(x)))=\frac{1}{\sqrt{x+\sqrt{x}}}$

So we concluded that

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