Free Practice Question
PS · Problem Solving
705-805
Functions
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)?
Answer Choices
Correct answer marked belowA
0
B
2
C
4
12
Correct
E
Not necessarily one above
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Explanation
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Official Explanation
Official
We are given F(1)=4, F(4)=3 and F(F(x))=F(x+2)-3 for all integer x.
We need to find F(5).
Step 1: Find F(3).
Let x=1:
F(F(1)) = F(1+2)-3
F(4) = F(3)-3
3 = F(3)-3
F(3) = 6
Step 2: Find F(5).
Let x=3:…
We need to find F(5).
Step 1: Find F(3).
Let x=1:
F(F(1)) = F(1+2)-3
F(4) = F(3)-3
3 = F(3)-3
F(3) = 6
Step 2: Find F(5).
Let x=3:…
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What it tests
Your ability to evaluate and compose functions, including unusual defined operations.
Common trap
Applying function operations in the wrong order or ignoring domain restrictions.
Details
Difficulty
705-805
Type
PS
Category