Question

the one to one function g and h are defined as follows g={(-1,8),(1,3),(6,4),(8,5),(9,-9)}h(x)=x-8/7Find the following. g^-1 (8) = h^-1 (x) =(h • h^-1)(o) =

Answer 1

One to one function : if no two elements in the domain of f correspond to the same element in the range of f .

The function g and h are one to one function and defined as;

g={(-1,8),(1,3),(6,4),(8,5),(9,-9)}

`h(x)=(x-8)/(7)`

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3)

`\begin{gathered} (h\circ h^(-1))(0) \\ (h\circ h^(-1))(x)=h(h^(-1)(x)) \\ (h\circ h^(-1))(x)=h(7x+8) \\ (h\circ h^(-1))(x)=((7x+8)-8)/(7) \\ (h\circ h^(-1))(x)=(7x+8-8)/(7) \\ (h\circ h^(-1))(x)=(7x+0)/(7) \\ (h\circ h^(-1))(x)=x \\ \text{Substitute x = 0} \\ (h\circ h^(-1))(0)=0 \end{gathered}`

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