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The graphs of the functions f and g are represented in In the figure g

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The graphs of the functions f and g are represented in In the figure g  [#permalink]

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New post 21 Feb 2019, 12:40
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A
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C
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E

Difficulty:

  75% (hard)

Question Stats:

38% (02:43) correct 62% (03:07) wrong based on 21 sessions

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GMATH practice exercise (Quant Class 20)

Image

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)
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Re: The graphs of the functions f and g are represented in In the figure g  [#permalink]

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New post 22 Feb 2019, 07:15
fskilnik wrote:
GMATH practice exercise (Quant Class 20)

Image

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


Image


\(? = g\left( {g\left( { - 1} \right) + 1} \right) + f\left( {g\left( 3 \right) + 1} \right) = g\left( {A + 1} \right) + f\left( {B + 1} \right)\)


\(A\,\, = \,\,g\left( { - 1} \right) = 4\,\,\,\left[ {{\rm{figure}}} \right]\)

\({?_{{\rm{temp1}}}} = g\left( {A + 1} \right) = g\left( 5 \right)\)

\({\rm{line}}\,\,L\,\,:\,\,\left\{ \matrix{
\,{\rm{slop}}{{\rm{e}}_L} = {{3 - 0} \over {1 - 4}} = - 1 \hfill \cr
\,\left( {0,4} \right) \in \,\,L\,\,\,\, \Rightarrow \,\,\,\,{{y - 4} \over {x - 0}} = - 1 \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,L\,\,:\,\,y = 4 - x\)

\(\left( {5,g\left( 5 \right)} \right)\,\, \in \,\,L\,\,\,\,\, \Rightarrow \,\,\,\,\,{?_{{\rm{temp1}}}} = g\left( 5 \right) = 4 - 5 = - 1\)


\(B = g\left( 3 \right)\,\,\,:\,\,\,\,\left( {3,g\left( 3 \right)} \right) \in \,\,L\,\,\,\,\, \Rightarrow \,\,\,\,\,g\left( 3 \right) = 4 - 3 = 1\)

\({?_{{\rm{temp2}}}} = f\left( {B + 1} \right) = f\left( 2 \right) = {c^2}\)

\(\left( {1,3} \right) \in {\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,3 = f\left( 1 \right) = {c^1}\,\,\,\,\, \Rightarrow \,\,\,\,\,c = 3\)

\({?_{{\rm{temp2}}}} = f\left( 2 \right) = 9\)


\(?\,\,\, = \,\,\,{?_{{\rm{temp1}}}}\,\, + \,\,{?_{{\rm{temp2}}}}\,\,\, = \,\,\, - 1 + 9\,\,\, = \,\,\,8\)


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  [#permalink]

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New post 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)

Image

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


Image


\(? = g\left( {g\left( { - 1} \right) + 1} \right) + f\left( {g\left( 3 \right) + 1} \right) = g\left( {A + 1} \right) + f\left( {B + 1} \right)\)


\(A\,\, = \,\,g\left( { - 1} \right) = 4\,\,\,\left[ {{\rm{figure}}} \right]\)

\({?_{{\rm{temp1}}}} = g\left( {A + 1} \right) = g\left( 5 \right)\)

\({\rm{line}}\,\,L\,\,:\,\,\left\{ \matrix{
\,{\rm{slop}}{{\rm{e}}_L} = {{3 - 0} \over {1 - 4}} = - 1 \hfill \cr
\,\left( {0,4} \right) \in \,\,L\,\,\,\, \Rightarrow \,\,\,\,{{y - 4} \over {x - 0}} = - 1 \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,L\,\,:\,\,y = 4 - x\)

\(\left( {5,g\left( 5 \right)} \right)\,\, \in \,\,L\,\,\,\,\, \Rightarrow \,\,\,\,\,{?_{{\rm{temp1}}}} = g\left( 5 \right) = 4 - 5 = - 1\)


\(B = g\left( 3 \right)\,\,\,:\,\,\,\,\left( {3,g\left( 3 \right)} \right) \in \,\,L\,\,\,\,\, \Rightarrow \,\,\,\,\,g\left( 3 \right) = 4 - 3 = 1\)

\({?_{{\rm{temp2}}}} = f\left( {B + 1} \right) = f\left( 2 \right) = {c^2}\)

\(\left( {1,3} \right) \in {\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,3 = f\left( 1 \right) = {c^1}\,\,\,\,\, \Rightarrow \,\,\,\,\,c = 3\)

\({?_{{\rm{temp2}}}} = f\left( 2 \right) = 9\)


\(?\,\,\, = \,\,\,{?_{{\rm{temp1}}}}\,\, + \,\,{?_{{\rm{temp2}}}}\,\,\, = \,\,\, - 1 + 9\,\,\, = \,\,\,8\)


The correct answer is (E).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Status: GMATH founder
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The graphs of the functions f and g are represented in In the figure g  [#permalink]

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New post 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 "600-700 level" before trying the harder ones.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "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  [#permalink]

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New post 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 "600-700 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  [#permalink]

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New post 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.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "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   [#permalink] 26 Feb 2019, 09:52
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