1. Consider the function f(x) loga(x 5), where the domain is the set of all real
ID: 3145145 • Letter: 1
Question
1. Consider the function f(x) loga(x 5), where the domain is the set of all real numbers greater than 5, and the codomain is the set of all real numbers. If you were going to prove that this is onto, what would be your choice for x in that proof. (Do not do a full proof, just write what the choice for x would be.) 2. Consider the function f(x) = 4 + , where the domain is the set of all real numbers greater than 4, and the codomain is the set of all real numbers greater than 7. Prove that this function is onto Clearly show all steps of the proof, using the format shown in class.Explanation / Answer
Hi, Please refrain from asking multiple questions in one, this is against chegg policy.
1. given function is f(x)=log4(x-5),
now, to prove f in onto, we have to show that every element in co-domain, there is an element in domain that maps to it, since this is an existential proof, we canot prove it by example, so thats why we reverse map the function and choose x,
let y=log4(x-5), now we write x in terms of y,
x-5=4y
i.e x=5+4y
this is the value we choose for the proof
2. To prove A functon i onto, we choose x in terms of y, given function is
y=4+(x+5)1/2, now we need to find x in terms of y,
i.e x=(y-4)2-5
, now since given y is set of all real numbers >7,
when y>7, x>9-5=4,
such that f((y-4)2-5)=y
hence the funcion is Onto
Thumbs up if this was helpful, otherwise let me know in comments
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