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Let f(x)=xx  for x0

(a) Find all x0 such that f(x)=1.

(a) Find all x0 such that f(x)=3.

(b) Find all x0 such that f(x)=5.

(c) Find the number of possible values of f(x) for 0x10.

 

Prove your answer

 May 22, 2022
 #1
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Letf(x)=xxforx0(a)findallx0suchthatf(x)=1

 

If  0<=x<1 then  f(x)=0

If  1<=x<2 then   f(x)= floor of (x*1) = 1

If x>=2      then    f(x)>1

 

so      if1x<2thenf(x)=1

 

(b)   

Letf(x)=xxforx0(a)findallx0suchthatf(x)=3

 

let0δ<1Ifx=2+δthenxx=(2+δ)2)=(4+2δ)=4or5

 

So if  x is 1 and a bit then f(x)=1

If x=2 and a bit then f(x)=4 or 5

f(x) cannot equal 3

 

You can think about the rest yourself.

 May 23, 2022

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