求$$$f{\left(x \right)} = - 3 x$$$與$$$g{\left(x \right)} = 5 x - 6$$$的複合函數
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求 $$$f{\left(x \right)} = - 3 x$$$ 與 $$$g{\left(x \right)} = 5 x - 6$$$ 的合成。
解答
$$$\left(f\circ g\right)\left(x\right) = f\left(g\left(x\right)\right) = f\left(5 x - 6\right) = - 3 {\color{red}\left(5 x - 6\right)} = 18 - 15 x$$$
$$$\left(g\circ f\right)\left(x\right) = g\left(f\left(x\right)\right) = g\left(- 3 x\right) = 5 {\color{red}\left(- 3 x\right)} - 6 = - 15 x - 6$$$
$$$\left(f\circ f\right)\left(x\right) = f\left(f\left(x\right)\right) = f\left(- 3 x\right) = - 3 {\color{red}\left(- 3 x\right)} = 9 x$$$
$$$\left(g\circ g\right)\left(x\right) = g\left(g\left(x\right)\right) = g\left(5 x - 6\right) = 5 {\color{red}\left(5 x - 6\right)} - 6 = 25 x - 36$$$
答案
$$$\left(f\circ g\right)\left(x\right) = 18 - 15 x$$$A
$$$\left(g\circ f\right)\left(x\right) = - 15 x - 6$$$A
$$$\left(f\circ f\right)\left(x\right) = 9 x$$$A
$$$\left(g\circ g\right)\left(x\right) = 25 x - 36$$$A