What is the smallest real number x in the domain of the function g(x) = sqrt(x^2 - (x - 15)^2)?

Guest May 23, 2021

#1**0 **

**What is the smallest real number x in the domain of the function \(g(x) = \sqrt{(x^2 - (x - 15)^2)}\)?**

Two reasons why a number might not be included in the domain is that it makes an expression in the denominator of a fraction equal to 0, or it makes the expression be the square root of a negative number. These are big no-nos.

Keeping this in mind, let's find what values of x *don't* work, so then we can find the ones (the smallest one in particular) that do. For x not to work, we would have to have:

\(\sqrt{x^{2}-(x-15)^{2}} < 0\).

Simplifying, we get:

\(-30x+225<0\)

\(30x<225\).

I'll let you finish!

Guest May 23, 2021