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1 .Function  is defined as follows:

\(\[g(x) = \left\{ \begin{array}{cl} 5x^2 & \text{if } x \le -3, \\ 21+x& \text{if }-3 < x \le 10, \\ 2-\sqrt{x}& \text{if }x > 10. \end{array}\right.\]\)

This function has an inverse.

What is \(g^{-1}(-7)\)

 

 

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

\(\[C(n) = \begin{cases} \dfrac n 2 & \text{if $n$ is even}, \\ 3n+1 & \text{if $n$ is odd}. \end{cases}\]\)

Find the smallest positive integer m such that \(C^m(9) = 1\)

 

2b. Find all n such that \(C^3(n) = 16\)

 Apr 17, 2022
 #1
avatar+124598 
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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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