Answer
1) $\frac{3}{\sqrt[3] 4+1}$
2) 1
3) 1.2
4) 0
Work Step by Step
If f and g are two functions, then the composite function is denoted by f o g,
1) First evaluate g(4) and then evaluate f(g(4))
g(x) = $\sqrt[3] x$
g(4) = $\sqrt[3] 4$
f(x) = $\frac{3}{x+1}$
f(g(x)) = $\frac{3}{g(x) + 1}$
f(g(4)) = $\frac{3}{\sqrt[3] 4+1}$
2) First evaluate f(2) and then evaluate g(f(2))
f(x) = $\frac{3}{x+ 1}$
f(2) = $\frac{3}{2+ 1}$ =1
g(x) = $\sqrt[3] x$
g(f(2)) = $\sqrt[3] 1$
g(f(2)) = 1
3) First Evaluate f(1). Substitute the answer into f to evaluate f(f(1))
f(x) = $\frac{3}{x+ 1}$
f(f(x)) = $\frac{3}{f(x)+ 1}$ = $\frac{3}{ \frac{3}{x+ 1}+ 1}$
f(f(1)) = $\frac{3}{ \frac{3}{1+ 1}+ 1}$
f(f(1)) = 1.2
4) First evaluate g(0). Substitute the answer into g to evaluate g(g(0))
g(x) = $\sqrt[3] x$
g(0) =$\sqrt[3] 0$ = 0
g(g(x)) = $\sqrt[3] g(x)$
g(g(0)) = $\sqrt[3] g(0)$ =$\sqrt[3] 0$
g(g(0)) = 0
