3f(x)=f(3x+1)-1 -> 3f(2)=f(6+1)-1 -> 3*5=f(7)-1 -> 16=f(7)yellowho wrote:The function f(x) is such that f(3x+1) = 3f(x) + 1 for all values of x. If f(2)=5, then f(7)=?
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Functions
Source: Beat The GMAT — Problem Solving |
Last edited by Night reader on Fri Jan 21, 2011 3:35 am, edited 1 time in total.
I don't know what you did there but I think you got the relationship backward.
My real question in this is, is there a way to solve this if 3x+1=7 is not true (X is not 2) as defined? Can you look at this like a sequence?
My real question in this is, is there a way to solve this if 3x+1=7 is not true (X is not 2) as defined? Can you look at this like a sequence?
Last edited by yellowho on Thu Jan 20, 2011 11:38 pm, edited 1 time in total.
The function f(x) is such that f(3x+1) = 3f(x) + 1 for all values of x. If f(2)=5, then f(7)=?
f(3x+1) = 3f(x)+1 => f(7) = f(3*2+1)
= 3 f(2) + 1 = 3*5+1 = 16
f(3x+1) = 3f(x)+1 => f(7) = f(3*2+1)
= 3 f(2) + 1 = 3*5+1 = 16
f(3x+1) = 3f(x) + 1 not 3x+1=7yellowho wrote:I don't know what you did there but I think you got the relationship backward.
My real question in this is, is there a way to solve this if 3x+1=7 is not true (X is not 2) as defined? Can you look at this like a sequence?
f(2)=5 is different function
we need to find yet another function f(7)
I tried my best, though it's nonstandard algebra application rather than backward restatement.
We know f(2) and our target is to determine the value of f(7). How we can do that?yellowho wrote:The function f(x) is such that f(3x+1) = 3f(x) + 1 for all values of x. If f(2)=5, then f(7)=?
One quiet obvious way is to express f(7) in terms of f(2). Can we do that? Yes! From the relations given, we can do that easily. How?
Just put x = 2 in the given relation.
Now we have, f(3x + 1) = 3f(x) + 1
=> f(3*2 + 1) = 3f(2) + 1
=> f(7) = 3f(2) + 1
Now we have f(7) in terms of f(2).
Just put the value of f(2), and we have f(7) = 3*5 + 1 = 16
How will you justify that step?Night Reader wrote:f(2)=f(6+1)=3f(2)+1 = 5 -> f(7)=3f(2)+1-5 -> f(7)=3f(2)-4
What you've wrote is equivalent to f(2) = f(7)
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
sorry didnt mean to offend. i just didn't understand what u did. that doesnt mean you are wrong tho. i posted this question to look for different ways to solve so a different approach is welcome.
thanks Rahul, I have edited my solution.Rahul@gurome wrote:We know f(2) and our target is to determine the value of f(7). How we can do that?yellowho wrote:The function f(x) is such that f(3x+1) = 3f(x) + 1 for all values of x. If f(2)=5, then f(7)=?
One quiet obvious way is to express f(7) in terms of f(2). Can we do that? Yes! From the relations given, we can do that easily. How?
Just put x = 2 in the given relation.
Now we have, f(3x + 1) = 3f(x) + 1
=> f(3*2 + 1) = 3f(2) + 1
=> f(7) = 3f(2) + 1
Now we have f(7) in terms of f(2).
Just put the value of f(2), and we have f(7) = 3*5 + 1 = 16
How will you justify that step?Night Reader wrote:f(2)=f(6+1)=3f(2)+1 = 5 -> f(7)=3f(2)+1-5 -> f(7)=3f(2)-4
What you've wrote is equivalent to f(2) = f(7)
