frozenbananas said:the composite is simply g then? or is it f(x) multiplied by g(x)?
A composite function is a combination of two or more functions, where the output of one function becomes the input of the next function. It is denoted as f(g(x)), which means the function f is applied to g(x).
To evaluate a composite function, you need to substitute the inner function's output as the input for the outer function. For example, if f(x) = x^2 and g(x) = 3x+1, then f(g(x)) = f(3x+1) = (3x+1)^2 = 9x^2 + 6x + 1.
The order of operations for composite functions is innermost to outermost. This means that you should evaluate the inner function first and then use the result as the input for the outer function.
Yes, you can simplify a composite function by using algebraic techniques such as factoring, distributing, and combining like terms. This can help make the function easier to evaluate and understand.
Composite functions are used in many real-life scenarios, especially in mathematical modeling. For example, in economics, the demand for a product can be modeled as a composite function of factors such as price, income, and advertising. In physics, the position of an object can be modeled as a composite function of time and velocity.