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

$$f\left(z\right)=\frac{3z+1}{2-4z}$$$$f\left(f\left(z\right)\right)=...$$

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

$$fof\left(z\right)=\frac{3f\left(z\right)+1}{2-4f\left(z\right)}=\frac{3\frac{3z+1}{2-4z}+1}{2-4\frac{3z+1}{2-4z}}=\frac{9z+3+2-4z}{4-8z-12z-4}=\frac{5z+5}{-20z}$$$$\Rightarrow fof\left(z\right)=-\frac{z+1}{4z}.$$

Answered by ajfour last updated on 09/Nov/18

$$f\left(f\left(z\right)\right)=\frac{3\left(\frac{3z+1}{2-4z}\right)+1}{2-4\left(\frac{3z+1}{2-4z}\right)}$$$$=\frac{5z+5}{-20z}=-\left(\frac{z+1}{4z}\right).$$

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