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What is f(g(4))?
That means that function "g" is first applied to the number 4. Then, the result of that is used with function "f".
What is a relation where x only has one y?
A Function. That is the definition of a function. I like to think of a function, f(x) as a number crunching machine. the number crunching machine eats different x 's. It eats each and every x and crunches it the same way, but spits out a new Y every time. Remember, y = f(x). That is, "y is a function of x". There you go.
How do you get a function of a function?
A function is a mapping from one set of numbers (domain) to another (range). The mapping need not be linear: it can be any mathematical function. That is, for every number in the domain the function provides a rule which allows you to calculate another number.If, then, you devise another function which is a mapping from the range of the first function to some other set, you have a function of a function.For example, suppose the first function, f, is "add 1" and the second function, g, is "square the number."Then the functiong of f = g[f(x)] = g[x+1] = [x+1]2 = x2 + 2x + 1however, note thatf of g = f[g(x)] = f[x2] = x2 + 1This illustrates that f of g is not the same as g of f.
How do you determine the range of f?
I assume the question is about the range of a function f. First, determine the domain of the function f. This is the set of all inputs. Use this information to find all the output values of f: that is the range. In most cases, you will not have to evaluate f for each and every input: the nature of f will help you.
What is recursive function?
A recursive function is one in which the value of a function at each point depends on its value at one or more previous points. A rercursive function requires the first few values to be defined normally - these are called bases. Perhaps one of the most famous recursive function is the Fibonacci series, which has f(1) = 1 f(2) = 1 f(n) = f(n-1) + f(n-2) for n = 3, 4, 5, ... There are two bases and each subsequent value is defined in terms of the preceding two.
