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0
190
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avatar+598 

Suppose the function $f$ has all real numbers in its domain and range and is invertible. Some values of $f$ are given by the following table: \($$\begin{array}{c || c | c | c | c | c} x & 1 & 2 & 3 & 4 & 5 \\ \hline f(x) & 2 & 3 & 5 & 7 & 8 \end{array}$$\)What is the value of $f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5))?$ If there is not enough information to answer this question, enter "NEI".

michaelcai  Nov 3, 2017
 #1
avatar+543 
-1

I think it is

 

3f^2+4+5/f^2

 

I hope!

ProMagma  Nov 3, 2017
 #2
avatar+86859 
+1

\(f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5))\)

 

f (3)  = 5

 

So   f(f(3))  =  f(5)  =   8

 

f-1 (5)  = 3

 

So   f-1 ( f-1(5) )      =  f-1 (3)  =  2

 

But    f-1 (4)   is   unknown

 

So

 

NEI

 

 

 

cool cool cool

CPhill  Nov 3, 2017

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