In Exercises 1–30, find the domain of each function. f(x) = √(5x+35)

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Welcome back. I'm so glad you're here. We are given the function F of X equals the square root of 16 X plus 64. And we need to find the domain. Well, we've got a domain restriction here. Anything inside the radical must be greater than or equal to zero. Why? Because of that whole value inside the radical is a negative number. We're dealing with imaginary numbers and we don't want imaginary numbers as part of our domain. So how do we figure out what values for X would make that whole thing inside the radical a negative number. We're going to set the 16 X plus 64. The numbers inside the radical greater than or equal to zero. Then we're going to solve for X. So we'll subtract 64 from both sides. So we'll have 16 X is greater than or equal to negative 64 Will divide both sides by And we will get X must be greater than or equal to negative four. Let's draw this on a number line. If we're going from negative infinity all the way up to positive infinity, we have zero. Somewhere in the middle there X must be greater than or equal to negative four. Well, here's negative four. It could include negative force. I'll fill that in and greater than or equal to negative for that's going to be heading toward positive infinity. How do we express this domain in interval notation? We're going to start with negative four. So we use a bracket to indicate that it could be negative for the bracket means including negative four. Negative for the possibility. And it's going all the way up to infinity, and we close infinity with the parentheses because we never quite obtain infinity. We look at our answer choices and this matches with answer choice. C. Well done, we'll catch you on the next one.

In Exercises 1–30, find the domain of each function. f(x) = √(5x+35)

Verified Solution

Key Concepts

Domain of a Function

Square Root Function

Inequalities