What is the domain of f(x)?

Question

$f(x)= 1/((2x-1)+sqrt(x^2-3)$

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Answer 1 · 2017-12-31T18:16:06

$D(f)=(-oo,-3]uuu[3,oo)$

$I_1:(2x−1)+sqrt(x^2−3)!=0$
$I_2:x^2-3>=0$

$D(f)=I_1nnnI_2$

$2x−1+sqrt(x^2−3)!=0$

$sqrt(x^2−3)!=1-2x$

$x^2−3!=(1-2x)^2$

$x^2−3!=1-4x+4x^2$

$0!=4-4x+3x^2$

$3x^2-4x+4!=0$

$"discriminant"<0$

$=>I_1=RR$

$x^2-3>=0$

$(x-3)(x+3)>=0$

$I_2=(-oo,-3]uuu[3,oo)$

$D(f)=I_1nnnI_2=RRnnn((-oo,-3]uuu[3,oo))$

$D(f)=(-oo,-3]uuu[3,oo)$