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If \(f(x) = \frac{5x +2}{3x-5}\) and g(x) = x2 - 2x - 1, then the value of g(f(f(3))) is
1. 2
2. \(\frac{1}{3}\)
3. 6
4. \(\frac{2}{3}\)

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Correct Answer - Option 1 : 2

Calculation:

⇒ f (3) = (5 × 3 + 2)/(3 × 3 - 5) = 17/4

⇒ f (f (3)) = [5 × (17/4) + 2]/[3 × (17/4) - 5] = 3

⇒ g(f(f(3))) = 32 - 2 × 3 - 1 = 9 - 6 - 1 = 9 - 7 = 2

∴ The required result will be 2.

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