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...)
Other useful lessons:
(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 yvalue answers) of one function becomes
the domain (the xvalues) 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'.
Remember:
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/
(2x1) is x 1/2.
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