How do you find the domain of #f(x) = arc cot( (x−1) / ((1−x)^0.5) ) + log_(1/3) (2x + 21)#?

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Answer 1 · 2016-07-11T15:33:22

Domain: #(-10 1/2, 1)#

The given equation is
#f(x)=cot^-1((x-1)/(1-x)^0.5)+log_(1/3) (2x+21)#

For the term #cot^-1((x-1)/(1-x)^0.5)#

Domain: #(-oo, 1)#

For the term #log_(1/3) (2x+21)#

Domain: #(-10 1/2, +oo)#

Therefore the domain for the entire equation is the intersection which is

Domain: #(-10 1/2, 1)#

God bless....I hope the explanation is useful.