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Guest Nov 16, 2014

#1
+19207
+5

$$\small{\text{  \begin{array}{rcl} f(x)=x+2 \\ f^{-1}(x) &=& ? \\ y & =& x+2 \quad | \quad x\leftrightarrow y \\ x & = & y+2 \\ y & = & x-2 \\ f^{-1}(x) & = & x-2 \\ \hline \\ g(x)=\dfrac{x}{3} \\ \\ g^{-1}(x) &=& ? \\ y & =& \dfrac{x}{3} \quad | \quad x\leftrightarrow y \\ \\ x & = & \dfrac{y}{3} \\ \\ y & = & 3x \\ g^{-1}(x) & = & 3x \\ \hline \end{array}  }}$$

$$\small{\text{  \begin{array}{rcccl} f(19) & = & 19 + 2 & = & 21 \\ g(21) & = & \frac{21}{3} & = & 7 \\ f^{-1}(7) & = & 7-2 & = & 5 \\ f^{-1}(5) & = & 5-2 & = & 3 \\ g^{-1}(3) & = & 3*3 & = & 9 \\ f(9) & = & 9 + 2 & = & 11 \\ \end{array}  }}$$

$$f(g^{-1}(f^{-1}(f^{-1}(g(f(19)))))) = 11$$

heureka  Nov 17, 2014
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#1
+19207
+5
$$\small{\text{  \begin{array}{rcl} f(x)=x+2 \\ f^{-1}(x) &=& ? \\ y & =& x+2 \quad | \quad x\leftrightarrow y \\ x & = & y+2 \\ y & = & x-2 \\ f^{-1}(x) & = & x-2 \\ \hline \\ g(x)=\dfrac{x}{3} \\ \\ g^{-1}(x) &=& ? \\ y & =& \dfrac{x}{3} \quad | \quad x\leftrightarrow y \\ \\ x & = & \dfrac{y}{3} \\ \\ y & = & 3x \\ g^{-1}(x) & = & 3x \\ \hline \end{array}  }}$$
$$\small{\text{  \begin{array}{rcccl} f(19) & = & 19 + 2 & = & 21 \\ g(21) & = & \frac{21}{3} & = & 7 \\ f^{-1}(7) & = & 7-2 & = & 5 \\ f^{-1}(5) & = & 5-2 & = & 3 \\ g^{-1}(3) & = & 3*3 & = & 9 \\ f(9) & = & 9 + 2 & = & 11 \\ \end{array}  }}$$
$$f(g^{-1}(f^{-1}(f^{-1}(g(f(19)))))) = 11$$