Mathematics

# 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)=

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