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Difficulty:
55%
(hard)
Question Stats:
65% (02:08) correct
35%
(02:09)
wrong
based on 52
sessions
History
Date
Time
Result
Not Attempted Yet
If f(x) = (x-1)^2+3, which of the following is true for all x?
I. 2f(x) = f(x-1) + f(x+1)
II. f(2-x) = f(x)
III. f(x) = f(-x)
A. I only
B. II only
C. III only
D. None
E. I, II and III
Source: OptimusPrep
I. 2f(x) = f(x-1) + f(x+1)
II. f(2-x) = f(x)
III. f(x) = f(-x)
A. I only
B. II only
C. III only
D. None
E. I, II and III
Source: OptimusPrep
Can anyone help me understand what was wrong with my approach? 
Step 1: I picked the number (2) and substituted it in the function f(x) = (x-1)^2+3
f(2) = 1^2+3 = 4
Step 2: I. 2f(x) = f(x-1) + f(x+1)
2f(2) = 2*4 = 8
f(x-1) + f(x+1) = f(2-1) + f(2+1) = f(1) + f(3) ===> Substituting f(1)+f(3) in f(x) = (x-1)^2+3 would equal 3 + (2)^2+3 = 3+4+3 = 10
Therefore, not true.
Step 3: II. f(2-x) = f(x)
f(2-2) = f(2)
f(0) = f(2) ===> Substituting in f(x) = (x-1)^2+3, f(0) = 3, f(2) = 4
Not true.
Step 4: III. f(x) = f(-x)
f(-x) = f(-2) ===> Substituting in f(x) = (x-1)^2+3, f(-2)= (-3)^2 +3 = 9+3 = 12
and we know that f(x)= f(2) = 4
Therefore, not true.
Step 1: I picked the number (2) and substituted it in the function f(x) = (x-1)^2+3
f(2) = 1^2+3 = 4
Step 2: I. 2f(x) = f(x-1) + f(x+1)
2f(2) = 2*4 = 8
f(x-1) + f(x+1) = f(2-1) + f(2+1) = f(1) + f(3) ===> Substituting f(1)+f(3) in f(x) = (x-1)^2+3 would equal 3 + (2)^2+3 = 3+4+3 = 10
Therefore, not true.
Step 3: II. f(2-x) = f(x)
f(2-2) = f(2)
f(0) = f(2) ===> Substituting in f(x) = (x-1)^2+3, f(0) = 3, f(2) = 4
Not true.
Step 4: III. f(x) = f(-x)
f(-x) = f(-2) ===> Substituting in f(x) = (x-1)^2+3, f(-2)= (-3)^2 +3 = 9+3 = 12
and we know that f(x)= f(2) = 4
Therefore, not true.
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06 Jun 2015, 01:24
Kudos
Bookmarks
try this
f(x) = f(x) ^ 2
this is true for 0 and 1 but not true for all X.
The question demands whats true for ALL VALUES OF X
in such ques , you can t pick numbers
you have to solve algebrically.
I am attaching solution in a pdf below. Check that out.
Kudos please , if it helps
f(x) = f(x) ^ 2
this is true for 0 and 1 but not true for all X.
The question demands whats true for ALL VALUES OF X
in such ques , you can t pick numbers
you have to solve algebrically.
I am attaching solution in a pdf below. Check that out.
Kudos please , if it helps
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File comment: Algebric solution to the question
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Downloaded 119 times
06 Jun 2015, 03:05
Kudos
Bookmarks
rajgurinder
Thank you Raj. you answer really helped. :-D
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
