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)#