Question

The one to one functions G and H are defined as follow

G={(-8,1),(1,5),(4,-5)(8,-9)}
H(x)=3x+4
find the following 
g^-1(1)=
h^-1(x)=
(h^-1oh)(-2)=

Answer 1

`G=\{(-8,1),(1,5),(4,-5),(8,-9)\}\\\\\Rightarrow\ \ \ G^(-1)=\{(1,-8),(5,1),(-5,4),(-9,8)\}\ \ \ \Rightarrow\ \ \ g^(-1)(1)=-8\\\\H(x)=3x+4\ \ \ and\ \ \ D_H=R\\\\ 3x=H(x)-4\ \ \ \Rightarrow\ \ \ x= (H(x)-4)/(3)\\\\h^(-1)(x)= (x-4)/(3) \ \ \ and\ \ \ D_(h^(-1))=R\\\\\\(h^(-1)\circ h)(-2)=-2\\\\h^(-1)\bigg {(}h(-2)\bigg{)}=h^(-1)\bigg {(}3(-2)+4\bigg{)}=h^(-1)(-2)= (-2-4)/(3) = (-6)/(3) =-2`