Question #17c77

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Answer 1 · 2014-11-09T14:06:31

Rule 1: #sqrt{"nonnegative"}#

#7-ln(x-1) ge0#

by adding #ln(x-1)#,

#=> 7 ge ln(x-1)#

by raising #e# to both sides,

#=> e^7 ge e^{ln(x-1)}=x-1#

by adding #1#,

#=> e^7+1 ge x#

Rule2: #ln("positive")#

#x-1 > 0#

by adding #1#,

#=> x > 1#

Hence, the domain of the function is #(1, e^7+1]#.

I hope that this was helpful.