College Algebra
Given the two functions fff and ggg, find fgfgfg and identify the domain.
f(x)=xf\left(x\right)=\sqrt{x}f(x)=x, g(x)=x+17g\left(x\right)=x+17g(x)=x+17
(fg)(x)=x17+x\left(fg\right)\left(x\right)=\frac{\sqrt{x}}{17+x}(fg)(x)=17+xx, Domain: (−∞,0]\left(-\infty,0\right\rbrack(−∞,0]
(fg)(x)=17−x\left(fg\right)\left(x\right)=17-\sqrt{x}(fg)(x)=17−x, Domain: (0,∞)\left(0,\infty\right)(0,∞)
(fg)(x)=x+17x\left(fg\right)\left(x\right)=\sqrt{x}+17x(fg)(x)=x+17x, Domain: [0,∞)\left\lbrack0,\infty\right)[0,∞)
(fg)(x)=x(x+17)\left(fg\right)\left(x\right)=\sqrt{x}\left(x+17\right)(fg)(x)=x(x+17), Domain: [0,∞)\left\lbrack0,\infty\right)[0,∞)