# Thread: Domain and range of functions

1. ## 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????

2. ## Re: Domain and range of functions

Originally Posted by GorFree
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 $\displaystyle f(t)=\sqrt[3]{t}$ then the domain of $\displaystyle f$ is all real numbers as is the range.

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