f-z-3z-1-2-4z-f-f-z-

Question Number 47394 by gunawan last updated on 09/Nov/18

f (z) = \frac{3 z + 1}{2 - 4 z}

f (f (z)) = \dots

Commented by maxmathsup by imad last updated on 10/Nov/18

f o f (z) = \frac{3 f (z) + 1}{2 - 4 f (z)} = \frac{3 \frac{3 z + 1}{2 - 4 z} + 1}{2 - 4 \frac{3 z + 1}{2 - 4 z}} = \frac{9 z + 3 + 2 - 4 z}{4 - 8 z - 12 z - 4} = \frac{5 z + 5}{- 20 z}

\Rightarrow f o f (z) = - \frac{z + 1}{4 z} .

Answered by ajfour last updated on 09/Nov/18

f (f (z)) = \frac{3 (\frac{3 z + 1}{2 - 4 z}) + 1}{2 - 4 (\frac{3 z + 1}{2 - 4 z})}

= \frac{5 z + 5}{- 20 z} = - (\frac{z + 1}{4 z}) .

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