Given that f(3)=5, and f(3x)=f(x)+2 for all x, find f^-1(11)
N nch New member Joined Jul 17, 2013 Messages 6 Aug 11, 2013 #1 Given that f(3)=5, and f(3x)=f(x)+2 for all x, find f^-1(11)
D Deleted member 4993 Guest Aug 11, 2013 #2 nch said: Given that f(3)=5, and f(3x)=f(x)+2 for all x, find f^-1(11) Click to expand... My strategy would be to find f(x) → f-1(x) I see that from the given conditions f(3x) - f(x) = 2 then \(\displaystyle \dfrac{f(3x)-f(x)}{3x - x} \ = \dfrac {2}{3x-x} = \dfrac{1}{x}\) \(\displaystyle \dfrac{d}{dx}[f(x)] \ \)→\(\displaystyle \ \dfrac{1}{x}\) Thus f(x) = A*ln(x) + B Now solve for A and B from the given conditions and then calculate f-1(x) and hence f-1(11)
nch said: Given that f(3)=5, and f(3x)=f(x)+2 for all x, find f^-1(11) Click to expand... My strategy would be to find f(x) → f-1(x) I see that from the given conditions f(3x) - f(x) = 2 then \(\displaystyle \dfrac{f(3x)-f(x)}{3x - x} \ = \dfrac {2}{3x-x} = \dfrac{1}{x}\) \(\displaystyle \dfrac{d}{dx}[f(x)] \ \)→\(\displaystyle \ \dfrac{1}{x}\) Thus f(x) = A*ln(x) + B Now solve for A and B from the given conditions and then calculate f-1(x) and hence f-1(11)
D DrPhil Senior Member Joined Nov 29, 2012 Messages 1,383 Aug 11, 2013 #3 nch said: Given that f(3)=5, and f(3x)=f(x)+2 for all x, find f^-1(11) Click to expand... I would make a table of values of f(x), and see what value of x results in f(x)=11: f(3) = 5 f(3*3) = f(9) = f(3) + 2 = 7 f(3*9) = . . . . . .
nch said: Given that f(3)=5, and f(3x)=f(x)+2 for all x, find f^-1(11) Click to expand... I would make a table of values of f(x), and see what value of x results in f(x)=11: f(3) = 5 f(3*3) = f(9) = f(3) + 2 = 7 f(3*9) = . . . . . .
