Fungsi (fg)(x)\left(\frac{f}{g}\right)\left(x\right)(gf)(x) jika diketahui fungsi f(x)=2x2+x−21f\left(x\right)=2x^2+x-21f(x)=2x2+x−21 dan g(x)=x2−9g\left(x\right)=x^2-9g(x)=x2−9 adalah ....
2x+7x+3\frac{2x^{ }+7}{x^{ }+3}x+32x+7
2x+7x−3\frac{2x+7}{x-3}x−32x+7
(2x−3)(x−7)(x+3)(x−3)\frac{\left(2x-3\right)\left(x-7\right)}{\left(x+3\right)\left(x-3\right)}(x+3)(x−3)(2x−3)(x−7)
(2x−3)(x+7)(x+3)(x−3)\frac{\left(2x-3\right)\left(x+7\right)}{\left(x+3\right)\left(x-3\right)}(x+3)(x−3)(2x−3)(x+7)
(2x−3)(x+3)\frac{\left(2x-3\right)}{\left(x+3\right)}(x+3)(2x−3)
Diketahui:
f(x)=2x2+x−21f\left(x\right)=2x^2+x-21f(x)=2x2+x−21
g(x)=x2−9g\left(x\right)=x^2-9g(x)=x2−9
Ditanya:
(fg)(x)=?\left(\frac{f}{g}\right)\left(x\right)=?(gf)(x)=?
Jawab:
(fg)(x)\left(\frac{f}{g}\right)\left(x\right)(gf)(x) =f(x)g(x)=2x2+x−21x2−9 =(2x+7)(x−3)(x+3)(x−3)=2x+7x+3=\frac{f\left(x\right)}{g\left(x\right)}=\frac{2x^2+x-21}{x^2-9}\ =\frac{\left(2x+7\right)\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}=\frac{2x+7}{x+3}=g(x)f(x)=x2−92x2+x−21 =(x+3)(x−3)(2x+7)(x−3)=x+32x+7