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求 $$$f{\left(x \right)} = 2 x - 1$$$ 與 $$$g{\left(x \right)} = 3 x + 5$$$ 的和、差、積與商。
解答
$$$\left(f + g\right)\left(x\right) = {\color{red}\left(2 x - 1\right)} + {\color{red}\left(3 x + 5\right)} = 5 x + 4$$$
$$$\left(f - g\right)\left(x\right) = {\color{red}\left(2 x - 1\right)} - {\color{red}\left(3 x + 5\right)} = - x - 6$$$
$$$\left(f\cdot g\right)\left(x\right) = {\color{red}\left(2 x - 1\right)}\cdot {\color{red}\left(3 x + 5\right)} = \left(2 x - 1\right) \left(3 x + 5\right)$$$
$$$\left(\frac{f}{g}\right)\left(x\right) = \frac{{\color{red}\left(2 x - 1\right)}}{{\color{red}\left(3 x + 5\right)}} = \frac{2 x - 1}{3 x + 5}$$$
答案
$$$\left(f + g\right)\left(x\right) = 5 x + 4$$$A
$$$\left(f - g\right)\left(x\right) = - x - 6$$$A
$$$\left(f\cdot g\right)\left(x\right) = \left(2 x - 1\right) \left(3 x + 5\right)$$$A
$$$\left(\frac{f}{g}\right)\left(x\right) = \frac{2 x - 1}{3 x + 5}$$$A