Write out the functions given
[tex]\begin{gathered} g(x)=\frac{x+9}{5} \\ h=((-1,4),(1,2),(4,-1),(5,6),(8,7)) \end{gathered}[/tex]
Find (a)
[tex](a)g^{-1}(x)[/tex]
make x the subject of the function g(x) to get the inverse of g(x)
[tex]\begin{gathered} g(x)=\frac{x+9}{5} \\ x+9=5\times g(x) \\ x=5\times g(x)-9 \end{gathered}[/tex]
Substitute x for g(x) to get the inverse function of g(x). Therefore,
[tex]Hence,(a)g^{-1}(x)=5x-9[/tex][tex]\begin{gathered} (b)g^{-1}(1)=5(1)-9 \\ =5-9=-4 \\ \text{Therefore,} \\ g^{-1}(-1)=-4 \end{gathered}[/tex]
[tex]gg^{-1}(1)=g(-4)[/tex][tex]g(-4)=\frac{-4+9}{5}=\frac{5}{5}=1[/tex]
Hence,
[tex]g\mathrm{}g^{-1}(1)=1[/tex]
Find (c)
From the h function given,
[tex]h^{-1}(4)=-1[/tex]
Hence,
(a) g-¹= 5x - 9
(b) g.g-¹= 1
(c)h-¹ = -1
