Question

Determine a função inversa g(x) da função f(x)= x/2 - x,

Answer 1

Para determinarmos a função inversa, trocamos "x" por "y" e, então, isolamos "y".

Sendo assim, temos:

$y~=~\frac{x}{2}-x\\\\\\Trocando~"x"~por~"y":\\\\\\x~=~\frac{y}{2}-y\\\\\\Isolando~"y":\\\\\\x~=~y.\left(\frac{1}{2}-1\right)\\\\\\x~=~y~.~\frac{-1}{2}\\\\\\y~=~\frac{x}{\frac{-1}{2}}\\\\\\y~=~x~.~\frac{2}{-1}\\\\\\\boxed{y~=~-2x}$

Resposta: A função g(x), inversa de f(x), vale g(x) = -2x