If fx - 1-2x - 1-x - 1-2-f fx -2x - 1-2x - 3 provided that x - 3-2

f(x) = 12x + 1 f(f(x)) = 12[12x + 1] + 1 = 1 (2x + 1)2 + 2x + 1 = 2x + 12x + 3 ∴ f(f(x)) = 2x + 12x + 3 ...

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Definition of Function

If fx = 1/2...

Question

If $f (x) = \frac{1}{2 x + 1}, x \neq - \frac{1}{2}, f (f (x)) = \frac{2 x + 1}{2 x + 3}$ provided that $x \neq - \frac{3}{2}$

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∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} + x & x + 1 & x - 2 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

f (x) = 2 x

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f (x) = s i n^{- 1} (\frac{\sqrt{3}}{2} x - \frac{1}{2} \sqrt{1 - x^{2}}), - \frac{1}{2} \leq x \leq 1

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∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} + x & x + 1 & x - 2 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = a x - 12

a

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