Question

If the function f(x) has a domain of (g,h) and a range of (j,k), then what is the domain and range of g(x) = m(f(x)] + p?​

Answer 1

`Dom\{g(x)\} = Dom\{f(x)\} = (g, h)`.

`Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)`

Explanation:

From Mathematics we remember that the domain of a functions corresponds to the set of values of the independent variable (
`x` 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
`f(x)` and we must find the domain and range of
`g(x)`.

Domain

The domain of
`g(x)` is the domain of
`f(x)`. That is,
`Dom\{g(x)\} = Dom\{f(x)\} = (g, h)`.

Range

We have to define the bounds of the range of
`g(x)`, given that range
`f(x)` is modified by streching and horizontal translation operations:

Lower bound (
`f(x) = j`)

`g(x) = m\cdot j +p`

Upper bound (
`f(x) = k`)

`g(x) = m\cdot k +p`

In consequence, the range of
`g(x)` is
`Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)`