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

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Feb 21, 2019 11:30 am

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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

Answer: [spoiler]____(E)__[/spoiler]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Source: Beat The GMAT — Problem Solving | Thu Feb 21, 2019 11:30 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

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

by fskilnik@GMATH » Fri Feb 22, 2019 5:50 am

fskilnik@GMATH 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.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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