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

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ceceturner2012 ceceturner2012

30-05-2018
Mathematics

contestada

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

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jdoe0001 jdoe0001 · Answer 1 · 2018-06-01T22:57:02+02:00

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