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1 .Function  is defined as follows:

\[g(x)={5x2if x3,21+xif 3<x10,2xif x>10.\]

This function has an inverse.

What is g1(7)

 

 

2. Function C is defined on positive integers as follows:

\[C(n)={n2if n is even,3n+1if n is odd.\]

Find the smallest positive integer m such that Cm(9)=1

 

2b. Find all n such that C3(n)=16

 Apr 17, 2022
 #1
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+1

1.

 

Either 

 

5x^2  =   -7        impossible

or

21 + x  = -7    ⇒  x  =  -7 -21  =  -28   but this is not in the  domain of the  second function

or

2 - sqrt (x)    =  -7

 

So

sqrt (x) =  2 +7

sqrt (x)   =9        square both sides

x   =81              this is in the domain of the  third function

 

So   g-1(-7)  =   81

 

cool cool cool

 Apr 17, 2022
 #2
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Thank You!

Guest Apr 17, 2022

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