Question

When composing the models of two functions, how are the input/output units of the inside and outside functions related? When working with products of models, how are the input/output units of the models related? Explain, using examples, how the units help interpret the meaning of the derivative in context.

Please, need the answer ASAP.

Answer 1

The output of the inner function becomes input of the outer functions

For example where f is the cost of wood and g is the area of a square chunk of wood of length a so that

calculates the cost of square chunk of wood of length a

so in this case the input/outputs are not related themselves. But for this multiplication to make sense, the units of both outputs must be equal

For example, if f and g denote the length and breath of a rectangle made by buying a wood chunk of cost a then their units must be equal for to calculate area of the rectangle