Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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Domain and Range - Problem 2

Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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Finding the domain of a involved problem. So here we have y is equal to the square root of 3x minus 4; and we need to figure out just the domain. For this one we’re not going to worry about the range.

What we need to remember is our rules of square roots. We can’t take the square root of a negative number. So what that tells us is this inside; 3x minus 4, has to actually be greater than or equal to 0. Square root of 0 is 0 so we can actually include that. From here, we’ve taken our problem, found the domain of this and we turned into an inequality. We solve this as we would any other inequality. Add 4 to the other side, 3x is greater than or equal to 4. Divide by 3, x is greater than or equal to 4/3.

By knowing that we can’t take the square root of a negative number, we were able to figure out that our domain is everything greater than or equal to 4/3. So you could either write this, leave it just as this, say x is greater than or equal to 4/3. Or if you want, you can put it into interval notation; [4/3] hard bracket because it’s included to infinity. You probably don’t need to write both. It’s just the same way of writing the same exact answer. So by remembering square root can only be positive or 0, you’re able to figure out the domain.

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