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?​

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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?​

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Thiên Thanh 5 years 2021-08-11T23:18:14+00:00 1 Answers 18 views 0

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  1. MichaelMet
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    2021-08-11T23:19:27+00:00
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    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)

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