Final answer:
Function notation matches functions to their inputs using the variable inside the parentheses. To invert a mathematical function, we perform the inverse operation, such as taking a square root. The multiplication of even and odd functions follows specific rules that determine the nature of the resulting function.
Step-by-step explanation:
In function notation, we match functions with their correct inputs by looking at the variable inside the parentheses. For example, if we have a function denoted by f(h) = h - 7, the input to the function is h. Similarly, for h(g) = -4 g, the input is g. If we come across g(1) = 2f, we notice that 1 is the input to g, but there is no function given with 1 as the input, so this does not match any of the functions listed.
To "undo" or "invert" a mathematical function, we perform the inverse operation. For instance, if we have a squared term and need to find the base, we take the square root. This is demonstrated in solving for a side of a right triangle using the Pythagorean Theorem, where after finding a², we would take the square root to find a.
Even and odd functions also follow certain properties when multiplied together. An even function times an even function, or an odd function times an odd function, will result in an even function. These properties help to determine the nature of the resulting functions and can be helpful for analyzing function behavior.