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

Answer:

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

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

Step-by-step 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 $Ran \{g(x)\} = (m\cdot j+p,m\cdot k +p)$