Maths · Functions
Let be a function such that =1 \) and =x+f(3 x-3) \) for all Then find the value
Let \( f \) be a function such that \( f(3)=1 \) and \( f(3 x)=x+f(3 x-3) \) for all \( x \) Then find the value of \( \boldsymbol{f}(\boldsymbol{3 0 0}) \)
- A. 5500
- B. 10100
- C. 5050 \)
- D. 1,71,700
Step-by-step solution
Given f(3)=1 and f(3x)=x+f(3x-3). Let t=3x, then f(t)=t/3+f(t-3). This recurrence holds for multiples of 3. Compute f(3)=1, f(6)=2+1=3, f(9)=3+3=6, f(12)=4+6=10, f(15)=5+10=15. Pattern: f(3n)=n(n+1)/2. For n=100, f(300)=100*101/2=5050.
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