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Math Help - Domain and range of functions

  1. #1
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    Domain and range of functions

    Domain's and range's are a bit tricky for me. I have multiple questions in these two problems.

    Find the domain and range of:

    1. - f(x)=(4-x^2)^(1/3)

    For the domain - The value inside the square root needs to remain non negative so -2 greater than or equal to x less than or equal to 2. Correct?

    For the range - The lowest value would be when the value inside the square root is 0, which is when x is equal to -2 or 2, and the low part of the range is 0. For the upper range 2^(1/3)? Is this correct?

    2. - f(x)=ln(4-x^2)

    For the domain - you can't take the natural log of a non positive value so (4-x^2) is greater than 0 so the math goes something like...

    4-x^2>0
    -x^2>-4
    x^2<4
    (another question, what happens to the equality sign when you square both sides? the positive value stays the same and negative reverses?)
    -2<x<2

    For the range - No idea????
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  2. #2
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    Re: Domain and range of functions

    Quote Originally Posted by GorFree View Post
    Domain's and range's are a bit tricky for me. I have multiple questions in these two problems.
    Find the domain and range of: 1. - f(x)=(4-x^2)^(1/3)

    2. - f(x)=ln(4-x^2)
    If f(t)=\sqrt[3]{t} then the domain of f is all real numbers as is the range.

    If g(t)=\ln(t) then the domain of g is all positive real numbers and the range is all real numbers.
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