Question

Let r={0,1,2,3} be the range of h(x) =x-7. The domain of h inverse is?

Answer 1

Remember that if the function f(x) has domain S, range T and is injective then f(x) has inverse
`f^(-1)(x)` with domain the range of f(x), that is, T.

Since the funciton h(x)=x-7 is a line then is an injective function. Then h(x) has inverse
`h^(-1)(x)`. Since the range of h(x) is
`r=\{0,1,2,3\}`, then
`h^(-1)(x)` has domain the range of h(x), that is,
`r=\{0,1,2,3\}`.