AB x , where A and B are matrices and x is a vector , AB x could be thought of as B transforming x first , and then A transforming the result of B x . x B x A ( B x ) A ( B x ) Transformed by B first The result transformed by A Now consider the composition of real - valued functions , familiar from high school . Use the given functions f , g , and h below and carry out the requested computations . f ( x ) = 2 x + 4 g ( x ) = x 2 - 3 x h ( x ) = x x - 2 a. ? (? ( ? ) ) and ? ( ? ( ? ) ) b. ?(? ( 2 ) ) and ? ( ? ( 2 ) ) c. (? ( ? ) ) d. (? ( 0 ) ) and (? ( 1 ) ) e. ? (? ( ( ? ) ) ) f. Reflect on how composing these functions and evaluating at a value ( such as at 2 in part b ) is similar to what we saw with matrix multiplication through the Pat & Jamie Task on Wednesday . Write at least two thoughtful sentences . 4 . Let the matrices F and G be defined as below . Answer the following questions accordingly . ? = [ 1 0 2 2 1 0 0 3 4 ] , ? = [ 2 4 1 0 3 2 5 0 1 ] a. Let ? = [ 1 2 1 ] , and let G x = y. Compute G x and compute F y . b. Let [ 1 2 1 ] , and let F x = u. Compute F x and compute G u . c. Explain how parts a ) and b ) illustrate matrix multiplication as composition of functions . d. Explain how parts a ) and b ) illustrate that matrices F and G are not commutative . 5 . Let A be a 5 x 4 matrix and B be a 4 x 3 matrix . a. What is the domain of the transformation defined by B ? What is the codomain of the transformation defined by B ? b. What is the domain of the transformation defined by A ? What is the codomain of the transformation defined by A ? c. What is the domain of the transformation defined by AB ? What is the codomain of the transformation defined by AB ? d. Explain why the product BA is not defined . Ground your explanation in the concepts of composition of functions , domain , and codomain