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November 12th, 2017, 05:51 AM  #1 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,672 Thanks: 120 Math Focus: Trigonometry and Logarithm  Which f(x) to use?
I hope you can read the questions clearly: For x = 2 and x = 0, which f(x) to use for each of them? I am confused because both of them are turning points. 
November 12th, 2017, 06:26 AM  #2 
Member Joined: Oct 2016 From: Slovenia, Europe Posts: 52 Thanks: 5 
I think we can't read it ... However, I can't.

November 12th, 2017, 07:17 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,119 Thanks: 2369 Math Focus: Mainly analysis and algebra 
$f(x)$ is continuous so you can just read off the graph. You don't need the slope.
Last edited by skipjack; November 12th, 2017 at 08:14 AM. 
November 12th, 2017, 09:12 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,445 Thanks: 1462  
November 12th, 2017, 05:22 PM  #5 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,672 Thanks: 120 Math Focus: Trigonometry and Logarithm  
November 12th, 2017, 06:04 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,119 Thanks: 2369 Math Focus: Mainly analysis and algebra 
Just look at the graph. $f(2)=0$ and $f(0)=2$.

November 12th, 2017, 07:38 PM  #7 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,672 Thanks: 120 Math Focus: Trigonometry and Logarithm 
So, (g o f o h)(2) = g(0) and (g o f o h)(0) = g(2)?

November 12th, 2017, 08:44 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 18,445 Thanks: 1462 
As h(2) = 5 and f(5) = 2, you should have obtained g(2) (which is 5), not g(0).

November 12th, 2017, 08:54 PM  #9 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,119 Thanks: 2369 Math Focus: Mainly analysis and algebra 
\begin{align*}&&(g \circ f \circ h)(2) &= g\bigg(f\big(h(2)\big)\bigg) \\ h(x)=x+3 \implies h(2) &= (2)+3 \\ &= 2+3 = 5 &\implies (g \circ f \circ h)(2) &= g\big(f(5)\big) \\ f(5) &= 2 & \implies (g \circ f \circ h)(2) &= g(2) & \text{(read from the graph)} \\ g(x) = 2x + 1 \implies g(2) &= 2(2)+1 \\ &= 5 &\implies (g \circ f \circ h)(2) &= 5 \\ \end{align*} 
November 12th, 2017, 10:07 PM  #10 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,672 Thanks: 120 Math Focus: Trigonometry and Logarithm 
I see, guess I made some mistakes last night.
