Simplify the Matrix

Problem

ƒ=[[x,0,1,2,3,4],[ƒ(x),3,2,0,1,4]],g=[[x,0,1,2,3,4],[g(x),1,4,3,0,2]],(ƒ∘g)*(2)

Solution

1. Identify the definition of the composition of functions.

(ƒ∘g)*(2)=ƒ*(g(2))

2. Evaluate the inner function g(2) by looking at the matrix for g

g(2)=3

3. Substitute the result of g(2) into the outer function ƒ

ƒ*(g(2))=ƒ(3)

4. Evaluate the function ƒ(3) by looking at the matrix for ƒ

ƒ(3)=1

Final Answer

(ƒ∘g)*(2)=1

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