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The graphs of the functions f and g are represented in In the figure g
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21 Feb 2019, 12:40
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GMATH practice exercise (Quant Class 20) The graphs of the functions f and g are represented in In the figure given. If f(x) = c^x (c constant), what is the value of g(g(1)+1) + f(g(3)+1)? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8
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Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our highlevel "quant" preparation starts here: https://gmath.net



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Re: The graphs of the functions f and g are represented in In the figure g
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22 Feb 2019, 07:15
fskilnik wrote: GMATH practice exercise (Quant Class 20) The graphs of the functions f and g are represented in In the figure given. If f(x) = c^x (c constant), what is the value of g(g(1)+1) + f(g(3)+1)? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 \(? = g\left( {g\left( {  1} \right) + 1} \right) + f\left( {g\left( 3 \right) + 1} \right) = g\left( {A + 1} \right) + f\left( {B + 1} \right)\) \(A\,\, = \,\,g\left( {  1} \right) = 4\,\,\,\left[ {{\rm{figure}}} \right]\) \({?_{{\rm{temp1}}}} = g\left( {A + 1} \right) = g\left( 5 \right)\) \({\rm{line}}\,\,L\,\,:\,\,\left\{ \matrix{ \,{\rm{slop}}{{\rm{e}}_L} = {{3  0} \over {1  4}} =  1 \hfill \cr \,\left( {0,4} \right) \in \,\,L\,\,\,\, \Rightarrow \,\,\,\,{{y  4} \over {x  0}} =  1 \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,L\,\,:\,\,y = 4  x\) \(\left( {5,g\left( 5 \right)} \right)\,\, \in \,\,L\,\,\,\,\, \Rightarrow \,\,\,\,\,{?_{{\rm{temp1}}}} = g\left( 5 \right) = 4  5 =  1\) \(B = g\left( 3 \right)\,\,\,:\,\,\,\,\left( {3,g\left( 3 \right)} \right) \in \,\,L\,\,\,\,\, \Rightarrow \,\,\,\,\,g\left( 3 \right) = 4  3 = 1\) \({?_{{\rm{temp2}}}} = f\left( {B + 1} \right) = f\left( 2 \right) = {c^2}\) \(\left( {1,3} \right) \in {\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,3 = f\left( 1 \right) = {c^1}\,\,\,\,\, \Rightarrow \,\,\,\,\,c = 3\) \({?_{{\rm{temp2}}}} = f\left( 2 \right) = 9\) \(?\,\,\, = \,\,\,{?_{{\rm{temp1}}}}\,\, + \,\,{?_{{\rm{temp2}}}}\,\,\, = \,\,\,  1 + 9\,\,\, = \,\,\,8\) The correct answer is (E). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.
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Re: The graphs of the functions f and g are represented in In the figure g
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25 Feb 2019, 04:23
Hi I am sorry could you please simplify your working out. I am a little confused on how you got to the final answer. fskilnik wrote: fskilnik wrote: GMATH practice exercise (Quant Class 20) The graphs of the functions f and g are represented in In the figure given. If f(x) = c^x (c constant), what is the value of g(g(1)+1) + f(g(3)+1)? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 \(? = g\left( {g\left( {  1} \right) + 1} \right) + f\left( {g\left( 3 \right) + 1} \right) = g\left( {A + 1} \right) + f\left( {B + 1} \right)\) \(A\,\, = \,\,g\left( {  1} \right) = 4\,\,\,\left[ {{\rm{figure}}} \right]\) \({?_{{\rm{temp1}}}} = g\left( {A + 1} \right) = g\left( 5 \right)\) \({\rm{line}}\,\,L\,\,:\,\,\left\{ \matrix{ \,{\rm{slop}}{{\rm{e}}_L} = {{3  0} \over {1  4}} =  1 \hfill \cr \,\left( {0,4} \right) \in \,\,L\,\,\,\, \Rightarrow \,\,\,\,{{y  4} \over {x  0}} =  1 \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,L\,\,:\,\,y = 4  x\) \(\left( {5,g\left( 5 \right)} \right)\,\, \in \,\,L\,\,\,\,\, \Rightarrow \,\,\,\,\,{?_{{\rm{temp1}}}} = g\left( 5 \right) = 4  5 =  1\) \(B = g\left( 3 \right)\,\,\,:\,\,\,\,\left( {3,g\left( 3 \right)} \right) \in \,\,L\,\,\,\,\, \Rightarrow \,\,\,\,\,g\left( 3 \right) = 4  3 = 1\) \({?_{{\rm{temp2}}}} = f\left( {B + 1} \right) = f\left( 2 \right) = {c^2}\) \(\left( {1,3} \right) \in {\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,3 = f\left( 1 \right) = {c^1}\,\,\,\,\, \Rightarrow \,\,\,\,\,c = 3\) \({?_{{\rm{temp2}}}} = f\left( 2 \right) = 9\) \(?\,\,\, = \,\,\,{?_{{\rm{temp1}}}}\,\, + \,\,{?_{{\rm{temp2}}}}\,\,\, = \,\,\,  1 + 9\,\,\, = \,\,\,8\) The correct answer is (E). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.



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The graphs of the functions f and g are represented in In the figure g
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25 Feb 2019, 06:26
menonrit wrote: Hi
I am sorry could you please simplify your working out. I am a little confused on how you got to the final answer.
Hi menonrit , Thank you for your interest in my solution. It has "10 lines". Feel free to ask for help for the FIRST line you didn´t understand. Tell me what you didn´t understand in that line, so that I will be able to help you in a productive way. Regards, Fabio. P.S.: if you don´t know even what to start asking, I suggest you study questions tagged as "600700 level" before trying the harder ones.
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Re: The graphs of the functions f and g are represented in In the figure g
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26 Feb 2019, 09:04
fskilnik wrote: menonrit wrote: Hi
I am sorry could you please simplify your working out. I am a little confused on how you got to the final answer.
Hi menonrit , Thank you for your interest in my solution. It has "10 lines". Feel free to ask for help for the FIRST line you didn´t understand. Tell me what you didn´t understand in that line, so that I will be able to help you in a productive way. Regards, Fabio. P.S.: if you don´t know even what to start asking, I suggest you study questions tagged as "600700 level" before trying the harder ones. Hi Fabio, Thank you for your message. Just wanted to know how you got "B = g(3)" and how did you get to the solution to "temp 2" Best regards, Ritvik



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Re: The graphs of the functions f and g are represented in In the figure g
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26 Feb 2019, 09:52
menonrit wrote: Hi Fabio,
Thank you for your message.
Just wanted to know how you got "B = g(3)" and how did you get to the solution to "temp 2"
Best regards,
Ritvik Hi, Ritvik. I am glad you are back! I have called g(3) as B, the same way I have called g(1) as A. (Check my first line, i.e., our FOCUS according to our "winning triad"!) As far as temp2 is concerned, please note that: (1) B equals g(3) that is equal to 1, hence B is equal to 1, hence B+1 is equal to 2 (2) f(B+1) must be f(2) and we know f(x) = c^x , hence f(2) = c^2 (3) We found c using the fact that the point (1,3) belongs to the curve y=f(x) If there is still something unclear, please let me know! Regards, Fabio.
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Re: The graphs of the functions f and g are represented in In the figure g
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