if f(x)=3 x and g(x)= 1/x , what is the domain of (g o f)(x)?

Question

if f(x)=3 x and g(x)= 1/x , what is the domain of (g o f)(x)?

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Margaret 5 days 2021-09-12T06:13:51+00:00 1 Answer 0

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    2021-09-12T06:15:47+00:00

    Answer:

    The domain is (-∞ , 0)∪(0 , ∞) OR The domain is {x : x ≠ 0}

    Step-by-step explanation:

    * Lets revise the composite function

    – A composite function is a function that depends on another function.

    – A composite function is created when one function is substituted into

     another function.

    – Ex: f(g(x)) is the composite function that is formed when g(x) is

     substituted for x in f(x).

    – In the composition (f ο g)(x), the domain of f becomes g(x).

    * Lets solve the problem

    ∵ f(x) = 3x and g(x) = 1/x

    – In (g o f)(x) we will substitute x in g by f

    ∴ (g o f)(x) = 1/3x

    – The domain of the function is all real values of x which make the

      function defined

    – In the rational function r(x) = p(x)/q(x) the domain is all real numbers

     except the values of x which make q(x) =0

    ∵ (g o f)(x) = 1/3x

    ∵ 3x = 0 ⇒ divide both side by 3

    ∴ x = 0

    ∴ The domain of (g o f)(x) is all real numbers except x = 0

    ∴ The domain is (-∞ , 0)∪(0 , ∞) OR The domain is {x : x ≠ 0}

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