College Algebra
Given the two functions fff and ggg, find fg\frac{f}{g}gf and identify the domain.
f(x)=14−3xf\left(x\right)=14-\frac{3}{x}f(x)=14−x3, g(x)=3xg\left(x\right)=\frac{3}{x}g(x)=x3
(fg)(x)=314x+1\left(\frac{f}{g}\right)\left(x\right)=\frac{3}{14}x+1(gf)(x)=143x+1, Domain: [0,∞)\left\lbrack0,\infty\right)[0,∞)
(fg)(x)=143x−1\left(\frac{f}{g}\right)\left(x\right)=\frac{14}{3}x-1(gf)(x)=314x−1, Domain: (−∞,0)∪(0,∞)\left(-\infty,0\right)\cup\left(0,\infty\right)(−∞,0)∪(0,∞)
(fg)(x)=3x−14\left(\frac{f}{g}\right)\left(x\right)=3x-14(gf)(x)=3x−14, Domain: (−∞,∞)\left(-\infty,\infty\right)(−∞,∞)
(fg)(x)=14x+3\left(\frac{f}{g}\right)\left(x\right)=14x+3(gf)(x)=14x+3, Domain: (−∞,∞)\left(-\infty,\infty\right)(−∞,∞)
