Bestimme die Komposition von $$$f{\left(x \right)} = 8 x^{2} - 10 x$$$ und $$$g{\left(x \right)} = 9 x - 7$$$

Bestimme die Komposition von $$$f{\left(x \right)} = 8 x^{2} - 10 x$$$ und $$$g{\left(x \right)} = 9 x - 7$$$.

$$$\left(f\circ g\right)\left(x\right) = f\left(g\left(x\right)\right) = f\left(9 x - 7\right) = 8 {\color{red}\left(9 x - 7\right)}^{2} - 10 {\color{red}\left(9 x - 7\right)} = 648 x^{2} - 1098 x + 462$$$

$$$\left(g\circ f\right)\left(x\right) = g\left(f\left(x\right)\right) = g\left(8 x^{2} - 10 x\right) = 9 {\color{red}\left(8 x^{2} - 10 x\right)} - 7 = 72 x^{2} - 90 x - 7$$$

$$$\left(f\circ f\right)\left(x\right) = f\left(f\left(x\right)\right) = f\left(8 x^{2} - 10 x\right) = 8 {\color{red}\left(8 x^{2} - 10 x\right)}^{2} - 10 {\color{red}\left(8 x^{2} - 10 x\right)} = 4 x \left(4 x - 5\right) \left(32 x^{2} - 40 x - 5\right)$$$

$$$\left(g\circ g\right)\left(x\right) = g\left(g\left(x\right)\right) = g\left(9 x - 7\right) = 9 {\color{red}\left(9 x - 7\right)} - 7 = 81 x - 70$$$

$$$\left(f\circ g\right)\left(x\right) = 648 x^{2} - 1098 x + 462$$$A

$$$\left(g\circ f\right)\left(x\right) = 72 x^{2} - 90 x - 7$$$A

$$$\left(f\circ f\right)\left(x\right) = 4 x \left(4 x - 5\right) \left(32 x^{2} - 40 x - 5\right)$$$A

$$$\left(g\circ g\right)\left(x\right) = 81 x - 70$$$A