Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (5 points) f(x) = x2 - 3 and g(x) = square root of 3+x

Answer 1

`\bf \begin{cases} f(x)=x^2-3\\ g(x)=√(3+x) \end{cases}\\\\ -------------------------------\\\\ f(~~g(x)~~)=[g(x)]^2-3\implies f(~~g(x)~~)=[√(3+x)]^2-3 \\\\\\ f(~~g(x)~~)=3+x-3\implies \boxed{f(~~g(x)~~)=x}\\\\ -------------------------------\\\\ g(~~f(x)~~)=√(3+[f(x)])\implies g(~~f(x)~~)=√(3+[x^2-3]) \\\\\\ g(~~f(x)~~)=√(3+x^2-3)\implies g(~~f(x)~~)=√(x^2) \\\\\\ \boxed{g(~~f(x)~~)=x}`