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Let $f(x)=x+1$ and $g(x)=2x$. Also denote the inverses to these functions as $f^{-1}$ and $g^{-1}$. Compute \[f(g^{-1}(f^{-1}(f^{-1}(g(f(5)))))).\]

Guest Nov 14, 2014

Best Answer 

 #1
avatar+80815 
+10

The inverse f is  y = x - 1      And the inverse of g is y = x/2

g(f(5) sanys to put 5 into f and then evaluate this in g =  2(5 +1) = 2(6)  = 12

And we want to put this result into the inverse of f = 12 - 1 = 11

And we want to put this result into f inverse, again  = 11 - 1 = 10

And we want to put this result into g inverse = 10/2 = 5

Finally, we want to put this result into f  = 5 + 1 = 6

 

CPhill  Nov 14, 2014
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2+0 Answers

 #1
avatar+80815 
+10
Best Answer

The inverse f is  y = x - 1      And the inverse of g is y = x/2

g(f(5) sanys to put 5 into f and then evaluate this in g =  2(5 +1) = 2(6)  = 12

And we want to put this result into the inverse of f = 12 - 1 = 11

And we want to put this result into f inverse, again  = 11 - 1 = 10

And we want to put this result into g inverse = 10/2 = 5

Finally, we want to put this result into f  = 5 + 1 = 6

 

CPhill  Nov 14, 2014
 #2
avatar+91412 
0

This looks like a mild brain strain - thanks Chris  :)

Melody  Nov 15, 2014

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