Question

For the real valued functions f and g are defined below find fog and gof Where

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

Answer 1

fog=f(g(x))=f(1/x²)=$\sqrt{1/x^2+1}$ =$\cfrac{\sqrt{x^2+1}}{\vert x\vert} ; x\isin\R$

gof=g(f(x))=$g(\sqrt{x+1})$ = $\cfrac{1}{x+1} ; x>-1$