Question

Sejam f(x) = x-8, g(x) = 3x+1 e h(x) = 2 + x². Determine

A) f o g

B) g o h

C) h[f(x)]

D) f[g(2)]

E) g[h(-1)]

Answer 1

$\left\{ \begin{array}{c} f(x)=x-8\\ \\ g(x)=3x+1\\ \\ h(x)=2+x^{2} \end{array} \right.$


A) $(f \circ g)(x)$

$(f \circ g)(x)=f[g(x)]\\ \\ (f \circ g)(x)=g(x)+8\\ \\ (f \circ g)(x)=(3x+1)+8\\ \\ (f \circ g)(x)=3x+9$


B) $(g \circ h)(x)$

$(g \circ h)(x)=g[h(x)]\\ \\ (g \circ h)(x)=3\cdot h(x)+1\\ \\ (g \circ h)(x)=3\cdot (2+x^{2})+1\\ \\ (g \circ h)(x)=6+3x^{2}+1\\ \\ (g \circ h)(x)=3x^{2}+7$


C) $h[f(x)]$

$h[f(x)]=2+[f(x)]^{2}\\ \\ h[f(x)]=2+(x-8)^{2}$


D) $f[g(2)]$

$f[g(2)]=(f\circ g)(2)\\ \\ f[g(2)]=3\cdot (2)+9\\ \\ f[g(2)]=6+9\\ \\ f[g(2)]=15$


E) $g[h(-1)]$

$g[h(-1)]=(g\circ h)(-1)\\ \\ g[h(-1)]=3\cdot (-1)^{2}+7\\ \\ g[h(-1)]=3\cdot 1+7\\ \\ g[h(-1)]=3+7\\ \\ g[h(-1)]=10$