Answer:
Correct choice is [tex]\dfrac{x+26}{5}[/tex]
Step-by-step explanation:
1. If [tex]F(x)=5x-6,[/tex] then you can find the inverse [tex]F^{-1}(x):[/tex]
[tex]y=5x-6,\\ \\5x=y+6,\\ \\x=\dfrac{y+6}{5},\\ \\F^{-1}(x)=\dfrac{x+6}{5}.[/tex]
2. If [tex]G(x)=x-4,[/tex] then
[tex]y=x-4,\\ \\x=y+4,\\ \\G^{-1}(x)=x+4.[/tex]
3. Hence,
[tex]G^{-1}(F^{-1}(x))=G^{-1}\left(\dfrac{x+6}{5}\right)=\dfrac{x+6}{5}+4=\dfrac{x+26}{5}.[/tex]
