Question

use the table below to find: (f ∘ g)(-1) = (g ∘ f)(10) = (f ∘ f)(-10) = (g ∘ g)(6) =

x	-10	-4	-1	2	5	6	9	10
f(x)	5	-1	-4	9	10	-10	2	6
g(x)	6	5	-10	2	9	-1	10	-4

question help: video

Explanation:

Step1: Recall composition formula

$(f\circ g)(x)=f(g(x))$ and $(g\circ f)(x)=g(f(x))$.

Step2: Calculate $(f\circ g)(-1)$

First find $g(-1)= - 10$. Then find $f(g(-1))=f(-10)=5$.

Step3: Calculate $(g\circ f)(10)$

First find $f(10)=6$. Then find $g(f(10))=g(6)= - 1$.

Step4: Calculate $(f\circ f)(-10)$

First find $f(-10)=5$. Then find $f(f(-10))=f(5)=10$.

Step5: Calculate $(g\circ g)(6)$

First find $g(6)= - 1$. Then find $g(g(6))=g(-1)= - 10$.

Answer:

$(f\circ g)(-1)=5$
$(g\circ f)(10)= - 1$
$(f\circ f)(-10)=10$
$(g\circ g)(6)= - 10$