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17 April, 10:55

Let f (x) = e^x and G (x) = x+6. What are the domain and range of g (f (x)) ?

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  1. 17 April, 11:02
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    Domain and Range of g (f (x)) are 'All real numbers' and y>6 respectively

    Step-by-step explanation:

    We have the functions, f (x) = eˣ and g (x) = x+6

    So, their composition will be g (f (x)).

    Then, g (f (x)) = g (eˣ) = eˣ+6

    Thus, g (f (x)) = eˣ+6.

    Since the domain and range of f (x) = eˣ are all real numbers and positive real numbers respectively.

    Moreover, the function g (f (x)) = eˣ+6 is the function f (x) translated up by 6 units.

    Hence, the domain and range of g (f (x)) are 'All real numbers' and y>6 respectively.
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