These expressions represent the composition of two functions, where one function is applied to the output of the other function. In other words, f(g(x)) means that the output of g(x) is used as the input for f(x), while g(f(x)) means that the output of f(x) is used as the input for g(x).
To solve these expressions, you need to apply the inner function first and then use the resulting output as the input for the outer function. This can be done by substituting the inner function into the outer function and simplifying the resulting expression.
Solving these expressions can help you understand the relationship between two functions and how they affect each other's outputs. It can also be useful in finding the inverse of a function.
Yes, in most cases, the outputs of f(g(x)) and g(f(x)) will be different. This is because the order of operations matters in function composition. The resulting outputs will only be the same if the two functions are inverses of each other.
The main difference between these expressions is the order in which the functions are applied. In f(g(x)), the function g(x) is applied first, while in g(f(x)), the function f(x) is applied first. This can result in different outputs and different mathematical interpretations.