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# 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

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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
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#1
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I think it is

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

I hope!

ProMagma  Nov 3, 2017
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$$f(f(3)) + f(f^{-1}(4)) + f^{-1}(f^{-1}(5))$$

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

CPhill  Nov 3, 2017

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