If f(x) = 2x/√(1-9x^2) and (fofo … f(x)) … 10 times = 2x/√(1-9αx^2) then

Question

If \(f(x) = \frac {2 x}{\sqrt {1 - 9 x^2}}\) and (fofo … f(x)) … 10 times \(=\frac {2x}{\sqrt {1 - 9 \alpha x^2}}\)then \(\sqrt {3\alpha + 1}\) is equal to 

(1) 1024 

(2) 512 

(3) 240 

(4) 108

Answer 1

Correct option is (1) 1024 

Notice that b_K is first difference G.P.

(S –1) = 4, (21 – 5) = 16, (85 – 21) = 64 

S_K = 1 + 5 + 21 + 85 + … + b₁₀ 

b_K = 1 + 5 + 21 + … + b₉ + b₁₀ 

O = 1 + 4 + 16 + 64 + … + … b₁₀ 

⇒ b₁₀ = 1 + 4 + 16 + 64 + …