<p>I know this isn't usually on the SAT, but I still want to know how to do this.</p>
<p>Find the domain of: 1/(2-rad(x^2-1))</p>
<p>*The stuff inside parentheses after rad means that its a radical expression</p>
<p>I know that the domain will be: ( -∞, -rad(5) ) UNION ( rad(5), ∞ ) but I also know that -1 and +1 will also work as values of x so how can I include them written in the domain?</p>
<p>the domain is all real number except -2, 2 and (-1,1)
Also u write sqrt() instead of rad(). All you have to do is make sure the denominator is not zero, nor let the the expression under the radical be negative.</p>
<p>The expression under the radical can be 0 but not negative, unless of course they want you to find an answer in imaginary numbers (not tested on reasoning).</p>
<p>You cannot let the denominator = 0. </p>
<p>That happens when 2-sqrt(x^2-1) =0, which is x^2-1=4, or x = +/- sqrt(5)</p>
<p>But you also cannot take the square root of a negative, so you need x^2-1 >= 0, which is x>=1 or x<=-1.</p>
<p>If you want to express the domain in interval notation, it gets ugly:</p>
<p>(-infinty, -sqrt(5)) U (-sqrt(5),-1] U [1,sqrt(5)) U ( sqrt(5), inifinty)</p>
<p>Much easier to say it in words: the domain is all real numbers with absolute value greater or equal to one, except + or - root 5.</p>
<p>Be glad this is never on the SAT.</p>