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Functions and domains. Please check my answers.

  1. Mar 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Question 1:
    Which of the following define y as a function of x on R (Real number). Explain for each why they are/ are not function.

    a) 4x^3 + y = 6
    b) x - y - square root x = 8
    c) x = cos^2 y
    d) y = (2x + 3) / (x - 1)

    Question 2:
    Let g(x) = sin(x) and h(x) = 1/x be defined on their natural domains. State the following, giving the domain for each function using set notation.

    a) 1 / h(x)
    b) (g ∘ h)(x)
    c) (h ∘ g)(x)
    d) h(x)g(x)

    2. Relevant equations
    None provided.


    3. The attempt at a solution

    Question 1
    a) y = 6 - 4x^3
    Function exists


    b) y = x - square root x - 8
    Function exists if x = R


    c) ?

    d) Function exits if x = R
    Function exists R \ {1}


    Question 2:
    a) 1 / (1/x) = x | x element R
    b) g(h(x)) = sin(1/x) | x ≠ infinity
    c) h(g(x)) = 1 / sin(x) | x ≠ 0
    d) (1/x)(sin(x)) = sin(x) / x | x ≠ 0

    OP's message:
    I am having trouble understanding how to do these questions and also to write down the reasons in a mathematical way...

    I have skipped the working since it will be difficult to type them. I will post a photo if necessary.
    Please explain the answer if they are wrong...
     
  2. jcsd
  3. Mar 23, 2014 #2

    haruspex

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    You mean, for any x in R? It doesn't say, but I think you're supposed to assume y must be real.
    What range of values can x have?
    So is the answer yes or no?
    1/h(x) cannot be defined at a value of x if h(x) is not defined there.
    You don't need to worry about x being infinity since infinity is not in R. What value of x is a problem?
    What value of sin(x) is disallowed for the function 1/sin(x)? For what value(s) of x does that happen?
    Right.
     
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