Question

Type the correct answer in the box. Consider functions f and g: f(x) = (x+1)^3g(x)= x^1/3 +1Evaluate the function composition. (fog)(–64) =

Answer 1

The composition

`(f\circ g)(x)`

Means that you have to evaluate x in g(x) first, and then evaluate that result in f(x)

In other words:

`(f\circ g)(x)=f(g(x))`

Let's use this for this question:

`\begin{gathered} f(x)=(x+1)^3 \\ g(x)=\sqrt[3]{x}+1 \\ \\ (f\circ g)(-64)=f(g(-64)) \\ \rightarrow g(-64)=-3 \\ \rightarrow f(-3)=-8 \\ \\ \text{Thereby} \\ (f\circ g)(-64)=-8 \end{gathered}`