fbpx
calculus online - Free exercises and solutions to help you succeed!

Domain of One Variable Function – A function with square root – Exercise 5738

Exercise

Determine the domain of the function:

y=\sqrt{3x-x^3}

Final Answer


x\leq -\sqrt{3}\text{  or  } 0\leq x\leq \sqrt{3}

Solution

Let’s find the domain of the function:

y=\sqrt{3x-x^3}

Because there is a square root, the expression inside the root must be non-negative:

3x-x^3\geq 0

Let’s find the roots of the polynomial equation:

3x-x^3=0

Factor the polynom:

x(3-x^2)=0

x(x-\sqrt{3})(x+\sqrt{3})=0

Therefore, its roots are

x=0,\pm\sqrt{3}

We are interested in the domain that holds this inequality:

x(x-\sqrt{3})(x+\sqrt{3})\geq 0

Therefore, the solution is

x\leq -\sqrt{3}\text{  or  } 0\leq x\leq \sqrt{3}

The polynom:

y=3x-x^3

looks like this:

פולינום ממעלה שלישית

The domain is marked in green lines.

Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions! 

Share with Friends

Leave a Reply