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# Finding the Domain of a Function - Problem 1

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

Let’s find the domain of a function. We got f(x) equals the quantity 1 plus root x times the quantity 4 minus root 9 minus x. For this function to be defined, we need both of these radicals to be defined. And this will be defined if x is greater than or equal to 0. This one will be defined if 9 minus x is greater than or equal to 0. And we need both of those to be true.

What does this mean? I can subtract 9 from both sides and get minus x is greater than or equal minus 9. Then I can multiply by -1. And of course doing so reverses the direction of the inequality. I get x is less or equal to 9 and I’ll reverse this; 0 is less than or equal to x.

Whenever you have 2 inequalities like this, they can be combined into a compound inequality. 0 is less than or equal to x is less than or equal to 9. And that means the domain of this function is the interval from 0 to 9.

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###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

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