Question

The domain of a function (x) is x < 5, and the range is y< 4. What are thedomain and range of its inverse function, h-11 (c)?A. Domain: x25Range: y24B. Domain: x < 5Range: y<4C. Domain: x24Range: y25D. Domain: x<4Range: yc5

Answer 1

We are given a function which domain is:

$D(h)=\mleft\lbrace x<5\mright\rbrace$

and its range is:

$R(h)=\mleft\lbrace y<4\mright\rbrace$

since the inverse of a function has a domain equal to the range of the original function we have that the range of the inverse of h is:

$D(h^{-1})=\mleft\lbrace x<4\mright\rbrace$

Since the range of an inverse function is the domain of the original function we have:

$R(h^{-1})=\mleft\lbrace y<5\mright\rbrace$