[tex]\bf \begin{cases} f(x) = x^2+1\\ g(x) = \sqrt{x-1} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(~~g(x)~~)=[g(x)]^2+1\implies f(~~g(x)~~)=[\sqrt{x-1}]^2+1 \\\\\\ f(~~g(x)~~)=\sqrt{(x-1)^2}+1 \\\\\\ f(~~g(x)~~)=x-1+1\implies \blacktriangleright f(~~g(x)~~)=x \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ g(~~f(x)~~)=\sqrt{[f(x)]-1}\implies g(~~f(x)~~)=\sqrt{[x^2+1]-1} \\\\\\ g(~~f(x)~~)=\sqrt{x^2}\implies \blacktriangleright g(~~f(x)~~)=x \blacktriangleleft[/tex]
