5B. Elementary Functions

Functions

You are familiar with functions from mathematics. For example, if f is defined by f (x) = x + 1, then f (2) = 3 and f (7) = 8.

You use functions in expressions. For example, if f (x) = x + 1, then expression f (3+2) + 1 has value 7. Evaluate an expression from the inside out.

f (3+2) + 1	=	f (5) + 1
	=	6 + 1
	=	7

and

f (4) + f (10)	=	5 + f (10)
	=	5 + 11
	=	16

Calling a function

An expression that uses a function is referred to as a function call.

Nested function calls

The argument of a function can be any expression, including an expression that uses a function. For example, if f (x) = x + 1, then

f (f (10))	=	f (11)
	=	12

and if g(x) = 2*x + 4, then

g(g(7) + f (2))	=	g(18 + f (2))
	=	g(18 + 3)
	=	g(21)
	=	46

Arguments/parameters

If E is an expression and f is a function, then we say that E is the argument of f in expression f (E). I will use term parameter interchangeably with argument.

Exercises

Suppose that g(x) = 3x - 2. What is the value of expression g(g(9) + 1)? Answer

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