Answer:
[tex]Dom\{g(x)\} = Dom\{f(x)\} = (g, h)[/tex].
[tex]Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)[/tex]
Step-by-step explanation:
From Mathematics we remember that the domain of a functions corresponds to the set of values of the independent variable ([tex]x[/tex] in this case) so that images exist and the range of a function is the set of images.
In this case, we know the domain and range of [tex]f(x)[/tex] and we must find the domain and range of [tex]g(x)[/tex].
Domain
The domain of [tex]g(x)[/tex] is the domain of [tex]f(x)[/tex]. That is, [tex]Dom\{g(x)\} = Dom\{f(x)\} = (g, h)[/tex].
Range
We have to define the bounds of the range of [tex]g(x)[/tex], given that range [tex]f(x)[/tex] is modified by streching and horizontal translation operations:
Lower bound ([tex]f(x) = j[/tex])
[tex]g(x) = m\cdot j +p[/tex]
Upper bound ([tex]f(x) = k[/tex])
[tex]g(x) = m\cdot k +p[/tex]
In consequence, the range of [tex]g(x)[/tex] is [tex]Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)[/tex]
