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The figure above shows the representations of the graphs of

by fskilnik@GMATH » Tue Mar 05, 2019 12:46 pm

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GMATH practice exercise (Quant Class 13)

Image

The figure above shows the representations of the graphs of the functions f and g, where f(x) = 2^(-0.5x) and g(x) = ax^2+b (a and b constants). What is the value of g(f(0)) ?

(A) 3
(B) 3.25
(C) 3.5
(D) 3.75
(E) 4

Answer: [spoiler]_____(D)___[/spoiler]
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by fskilnik@GMATH » Tue Mar 05, 2019 2:18 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 13)

Image

The figure above shows the representations of the graphs of the functions f and g, where f(x) = 2^(-0.5x) and g(x) = ax^2+b (a and b constants). What is the value of g(f(0)) ?

(A) 3
(B) 3.25
(C) 3.5
(D) 3.75
(E) 4
Image

$$? = g\left( {f\left( 0 \right)} \right)$$
$$\left[ {{\rm{blue}}} \right]\,\,\,\left( {0,f\left( 0 \right)} \right) \in {\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,f\left( 0 \right) = {2^{ - {1 \over 2}\left( 0 \right)}} = 1$$
$$? = g\left( 1 \right) = a \cdot {1^2} + b = a + b$$
$$\left[ {{\rm{red}}} \right]\,\,\,\,\left\{ \matrix{
\left( { - 4,b} \right) \in {\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,b = {2^{ - {1 \over 2}\left( { - 4} \right)}} = 4 \hfill \cr
\left( { - 4,0} \right) \in {\rm{graph}}\left( g \right)\,\,\,\,\,\mathop \Rightarrow \limits^{b = 4} \,\,\,\,\,0 = a \cdot {\left( { - 4} \right)^2} + 4\,\,\,\, \Rightarrow \,\,\,\,a = - {1 \over 4} \hfill \cr} \right.$$
$$? = - {1 \over 4} + 4 = 3.75$$


The correct answer is (D).


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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