Finding the Domain

[ebclassicalguitar]

Hi. I have never used this site before, but I am reviewing for Algebra in my Calculus class.


Find the Domain of:

(4x^2-2)


I can't figure it out to save my life. Thank you so much!

 

[Someone2841]

Hi. I have never used this site before, but I am reviewing for Algebra in my Calculus class.


Find the Domain of:

(4x^2-2)


I can't figure it out to save my life. Thank you so much!

The domain of a function is the set of all valid input variables. If we are assuming that \(\displaystyle f:\mathbb{R}\mapsto\mathbb{R}\) (the function \(\displaystyle f\) maps a real variable onto another) then the domain could be \(\displaystyle \left \{x:x\in\mathbb{R} \right \}\) (the set of x such that x is a real number) or, in inteval notation, \(\displaystyle (-\infty,\infty)\).


That's basically all to say any real number would produce another real number in your function, \(\displaystyle f(x) = 4x^2-2\).

Take \(\displaystyle g(x) = \sqrt{\frac{x}{x-10}}\). Assuming we want \(\displaystyle g:\mathbb{R}\mapsto\mathbb{R}\), it must hold that \(\displaystyle x > 10\). If x were less than ten, we would get an imaginary number (i.e., \(\displaystyle \sqrt{-1} = i\)). When \(\displaystyle x = 0\), we divide by zero which is undefined. We can write this as \(\displaystyle \{x:x>10\}\) or, in interval notation, \(\displaystyle (10,\infty)\)

 

[lookagain]

Take \(\displaystyle g(x) = \sqrt{\frac{x}{x-10}}\).

Assuming we want \(\displaystyle g:\mathbb{R}\mapsto\mathbb{R}\),

it must hold that \(\displaystyle x > 10\). If x were less than ten,

we would get an imaginary number (i.e., \(\displaystyle \sqrt{-1} = i\)).

When \(\displaystyle x = 0\), we divide by zero which is undefined.

We can write this as \(\displaystyle \{x:x>10\}\) or, in interval notation, \(\displaystyle (10,\infty)\)

Someone2841,

you are missing part of the domain.


x = 0 works, as well as any negative value of x.


\(\displaystyle The \ domain \ is \ x \ \le \ 0 \ or \ x > 10.\)


In interval notation, it is

\(\displaystyle (-\infty,0] \cup (10, \infty)\)