College Algebra
Given the two functions fff and ggg, find fg\frac{f}{g}gf and identify the domain.
f(x)=18xx−6,g(x)=16x+10f\left(x\right)=\frac{18x}{x-6},g\left(x\right)=\frac{16}{x+10}f(x)=x−618x,g(x)=x+1016
(fg)(x)=9x(x+10)8(x−6)\left(\frac{f}{g}\right)\left(x\right)=\frac{9x\left(x+10\right)}{8\left(x-6\right)}(gf)(x)=8(x−6)9x(x+10), (−∞,−10)∪(6,∞)\left(-\infty,-10\right)\cup\left(6,\infty\right)
(fg)(x)=9x(x+10)8(x−6)\left(\frac{f}{g}\right)\left(x\right)=\frac{9x\left(x+10\right)}{8\left(x-6\right)}(gf)(x)=8(x−6)9x(x+10), (−∞,−10)∪(−10,6)∪(6,∞) \left(-\infty,-10\right)\cup\left(-10,6\right)\cup\left(6,\infty\right) (−∞,−10)∪(−10,6)∪(6,∞)
(fg)(x)=9(x+10)8x(x−6)\left(\frac{f}{g}\right)\left(x\right)=\frac{9\left(x+10\right)}{8x\left(x-6\right)}(gf)(x)=8x(x−6)9(x+10),(−∞,−10)∪(−10,6)∪(6,∞) \left(-\infty,-10\right)\cup\left(-10,6\right)\cup\left(6,\infty\right)
(fg)(x)=9x(x−6)8(x+10)\left(\frac{f}{g}\right)\left(x\right)=\frac{9x\left(x-6\right)}{8\left(x+10\right)}(gf)(x)=8(x+10)9x(x−6),(−∞,−10)∪(−10,6)∪(6,∞) \left(-\infty,-10\right)\cup\left(-10,6\right)\cup\left(6,\infty\right)
