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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)=?
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?
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)=?
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
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)
