Algebra II: Composite functions
This is a free lesson from our course in Algebra II
In this lesson you'll explore beyond the earlier learnt concepts from lesson on functions, how such functions can be combined to give a composite function.
A function is a mathematical expression which changes one number into another. It always changes a number the same way. A composite function is a combination of two functions, where you apply the first function and get an answer, and then fill that answer into the second function. Suppose that f and g are two functions, the composition fg is defined by fg (x) = f(g(x)). (More text below video...)
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(Continued from above) To derive the composite function, steps to remember:
feed value to first function.
resulting value may be fed to second function.
take end result from second function.
In math terms, the range (the y-value answers) of one function becomes the domain (the x-values) of the nest function. The notation used for composition of functions is: (fog)(x) = f(g(x)). It is read as 'f composed with g of x' or 'f of g of x'.
Here the letters stay in the same order in each expression for the composition. You may note, f (g(x)) clearly indicates to start with function g (innermost parentheses are done first).
In cases of functions not defined for the real numbers are evaluated over a restricted domain. E.g. Domain of f(x) = (x - 2) is given by x - 2 >= 0. Rational expressions restrict only a few points, which make the denominator equal to zero. To find the domain of a function with a rational expression, set the denominator of the expression not equal to zero and solve for x. For example, domain of the function f(x) = (x + 2)(x - 3)/(x - 9)(2x + 8) (x + 8) is x 9, -4, -2. In case if there is a radical in the denominator, you may set the radicand to greater then zero and solve for x. E.g. domain of the function f(x) = 9/ (2x-1) is x 1/2.
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