$$f(x) = \frac{5x+2}{3x-5}$$ and $$g(x) = x^2 - 2x - 1$$, then the value of $$g(f(f(3)))$$ is

Solution

$$f(3) = \frac{15 + 2}{9 - 5} = \frac{17}{4}$$
$$f(f(3)) = \frac{5*17/4 + 2}{3*17/4 - 5} = \frac{93/4}{31/4} = \frac{93}{31} = 3$$
$$g(f(f(3))) = 3^2 - 3*2 - 1 = 2$$

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CAT 2017 Question Paper (Shift-1) Question 99

$$f(x) = \frac{5x+2}{3x-5}$$ and $$g(x) = x^2 - 2x - 1$$, then the value of $$g(f(f(3)))$$ is

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