Question

determine a função inversa das seguintes funções bijetoras de ℝ em ℝ: a) f(x) = x - 6 b) f(x) = 1 - 2x c) f(x) = 3x + 4 d) f(x) = 3x e) y = x - 3 f) y = x + 2/4​

Answer 1

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$\tt{a)}~\sf{f(x)=x-6}\\\sf{x=f(x)+6}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{f^{-1}(x)=x+6}}}}}\\\tt{b)}~\sf{f(x)=1-2x}\\\sf{2x=1-f(x)}\\\sf{x=\dfrac{1-f(x)}{2}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf f^{-1}(x)=\dfrac{1-x}{2}}}}}$

$\tt{c)}~\sf{f(x)=3x+4}\\\sf{3x=f(x)-4}\\\sf{x=\dfrac{f(x)-4}{3}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{f^{-1}(x)=\dfrac{x-4}{3}}}}}}\\\tt{d)}~\sf{f(x)=3x}\\\sf{x=\dfrac{f(x)}{3}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{f^{-1}(x)=\dfrac{x}{3}}}}}}$

$\tt{e)}~\sf{y=x-3}\\\sf{x=y+3}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{f^{-1}(x)=x+3}}}}}\\\tt{f)}~\sf{y=x+\dfrac{2}{4}}\\\sf{x=y-\dfrac{2}{4}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{f^{-1}(x)=x-\dfrac{2}{4}}}}}}$