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A dump of our free Chat sessions, in case it is useful. It excludes white boards used during paid sessions.

tutor3 : Hello Student, May I help you with your Math problems?
student : if f(f(5))=f(g(5)), which of the following must be true?
student : I. f(5) =g(5)
student : II. f(f(5))=g(f(5))
student : III. g(g(5))=g(f(5))
tutor3 : f(5)=g(5)
student : and how can you tell?
tutor3 : both functions are equal.it comes from the property of fucntions
student : What are the properties of functions?
tutor3 : if f(x)=f(y) then x=y
student : oh, but my answer options only say none of the above, II only, III only, I and II, or II and III
student : So would it have to be I and II only
student : ?
tutor3 : only 1
student : that's not one of my options though
student : why could't it be II?
tutor3 : because the question says f(f(5))=f(g(5))
student : you can't reverse the order of the g and f?
student : ?
student : No
student : And I suppose III is wrong because we're not given enough information to make that assumption?
tutor3 : Yes
student : The second part of the question is If 10x-8 =k(2x-1)-3 for all real numbers x, what is the value of k?
student : Is the answer 5 ?

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