Question

determine a inversa de cada função bijetora. a)f(x)=x-6
b)f(x)=1-2x

Answer 1

$f(x)=x-6\\\\ f(x)=y\\\\ y=x-6\\ x=y-6\\ y=x+6\\\\ \boxed{f(x)^{-1}=x+6}\\\\\\\\ f(x)=1-2x\\\\ f(x)=y\\\\ x=1-2y\\ -2y=x-1\\ 2y=-x+1\\\\ y= \dfrac{-x+1}{2} \\\\ y= -\dfrac{1}{2}x+ \dfrac{1}{2}\\\\\\ \boxed{f(x)^{-1}=- \dfrac{1}{2} x+ \dfrac{1}{2} }$