Ask Question
20 January, 00:47

If f (x) = 4x+3 and g (x) = the square root of x-9, which is true? 2 is in the domain of f of g or 2 is not in the domain of f of g?

+3
Answers (1)
  1. 20 January, 01:16
    0
    2 is not in the domain of f of g

    Step-by-step explanation:

    * Lets revise at first the meaning of f of g (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

    - Example:

    # 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)

    * Now lets solve the problem

    ∵ f (x) = 4x + 3

    ∵ g (x) = √ (x - 9)

    - Lets find f (g (x)), by replacing x in f by g (x)

    ∴ f (g (x)) = f (√ (x - 9)) = 4[√ (x - 9) ] + 3

    ∴ f (g (x)) = 4√ (x - 9) + 3

    ∵ The domain of f is g (x)

    - The domain of the function is the values of x which make the

    function defined

    ∵ There is no square root for negative values

    ∴ x - 9 must be greater than or equal zero

    ∵ x - 9 ≥ 0 ⇒ add 9 for both sides

    ∴ x ≥ 9

    ∴ The domain of f of g is all the real numbers greater than or equal 9

    ∴ The domain = {x I x ≥ 9}

    ∵ 2 is smaller than 9

    ∴ 2 is not in the domain of f of g
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “If f (x) = 4x+3 and g (x) = the square root of x-9, which is true? 2 is in the domain of f of g or 2 is not in the domain of f of g? ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers