Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))= F(x

Question

Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))=F(x+2)-3, for all integer values of x. What is the value of F(5)?

(A) 0
(B) 2
(C) 4
(D) 12
(E) Not necessarily one above

chetan2u · Answer

The functions required and some values given tells you that you have to find f(5) from rearranging the equation and substituting f(1) and f(4)..
Let us do step wise..

We are given f(x) and f(x+2), that is difference of 2, so let us find f(3)
Let x=1, so f(f1)=f(1+2)-3....f(4)=f(3)-3....f(3)=3+3=6

Now let us take x as 3 to find f(5)
F(f(3))=f(5)-3....f(6)=f(5)-3

But we have another function as f(6), which can be found by taking x as 4
F(f(4))=f(6)-3.....f(3)=f(6)-3....6=f(6)-3....f(6)=9

Substitute this in f(6)=f(5)-3....9=f(5)-3....f(5)=12

D

fskilnik · Answer

F\left( {F\left( x \right)} \right) = F\left( {x + 2} \right) - 3\,\,\,,\,\,\,x\,\,{\mathop{\rm int}} \,\,\,\,\,\left( * \right)

F\left( 1 \right) = 4\,\,,\,\,F\left( 4 \right) = 3\,\,\,\,\,\left( {**} \right)

? = F\left( 5 \right)

x = 3\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,F\left( {F\left( 3 \right)} \right) = F\left( 5 \right) - 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = F\left( {F\left( 3 \right)} \right) + 3

x = 1\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,F\left( {F\left( 1 \right)} \right) = F\left( 3 \right) - 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,F\left( 3 \right) = F\left( {F\left( 1 \right)} \right) + 3\,\,\mathop = \limits^{\left( {**} \right)} \,\,F\left( 4 \right) + 3\,\,\mathop = \limits^{\left( {**} \right)} \,\,3 + 3 = 6

? = F\left( 6 \right) + 3

x = 4\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,F\left( {F\left( 4 \right)} \right) = F\left( 6 \right) - 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,F\left( 6 \right) = F\left( {F\left( 4 \right)} \right) + 3\,\,\mathop = \limits^{\left( {**} \right)} \,\,F\left( 3 \right) + 3\,\, = \,\,6 + 3 = 9

? = F\left( 6 \right) + 3 = 9 + 3 = 12

The correct answer is (D).

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

Regards, 
Fabio

GMATWhizTeam · Answer

Solution

• It is given that:
 o   F(1) = 4 
o  F(4) = 3 
o  F(F(x)) = F(x + 2) – 3 …..Eq.(i) 
o x is an integer.  
We need to find F(5).
 • To find F(5), let’s substitute  x = 3  in Eq.(i), we get
 o  F(F(3)) = F(5) – 3 ⟹ F(5) = F(F(3)) + 3 ……Eq.(ii)  
• To find F(3), let’s substitute  x = 1  in Eq.(1), we get,
 o  F(F(1)) = F(1+2) – 3 ⟹ F(3) = F(4) + 3 ⟹ F(3) = 3+3 = 6  
• Now, substituting the above value of F(3) in Eq.(ii) we get,
 o  F(5) = F(6) + 3……Eq.(iii)  
• To find F(6) let’s substitute  x = 4  in the Eq.(i), we get,
 o  F(F(4)) = F(4+2) – 3 ⟹ F(6) = F(3) + 3 ⟹F(6) = 6 + 3 = 9  
• Substituting the value of F(6) in Eq.(iii), we get,
 o  F(5) = 9 + 3 = 12   
Thus, the correct answer is  Option D.

rvgmat12 · Answer

f(f(1)) = f(3)-3

f(3) = 3+3 = 6

f(f(3)) = f(5)-3
f(6)=f(5) -3

f(f(4)) = f(6)-3
f(3)=f(6)-3

f(6)=9

f(5) = 12

D

ScottTargetTestPrep · Answer

Let's substitute x = 1 in F(F(x)) = F(x + 2) - 3:

\Rightarrow  F(F(1)) = F(1 + 2) - 3

\Rightarrow  F(4) = F(3) - 3

\Rightarrow  3 = F(3) - 3

\Rightarrow  6 = F(3)

Now, let's substitute x = 4 in F(F(x)) = F(x + 2) - 3:

\Rightarrow  F(F(4)) = F(4 + 2) - 3

\Rightarrow  F(3) = F(6) - 3

\Rightarrow  6 = F(6) - 3

\Rightarrow  9 = F(6)

Finally, let's substitute x = 3 in F(F(x)) = F(x + 2) - 3:

\Rightarrow  F(F(3)) = F(3 + 2) - 3

\Rightarrow  F(6) = F(5) - 3

\Rightarrow  9 = F(5) - 3

\Rightarrow  12 = F(5)

Answer: D

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Winston created a function F such that F(1)=4, F(4)=3 and F(F(x))= F(x

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