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1.4 Standard Functions

A standard function is one defined on an interval of ℝ that is obtained by a finite sequence of standard operations starting from any combination of three basic functions .

What are the basic functions ?

The identity function f ( x ) = x

The exponential function f ( x ) = exp ⁡ ( x )

The sine function f ( x ) = sin ⁡ ( x )

What are the standard operations?

Multiplication by a number in ℝ , addition, subtraction, multiplication, division, substitution of the value of one function as argument of another, and taking the "inverse".

Most of the functions we encounter will be standard functions.

Examples: 4 x 2 , x sin ⁡ ( x ) , exp ⁡ ( sin ⁡ x ) x .

You can enter your favorite standard functions, f and g , in the following applet, and observe the effects of combining f and g in various ways, and also look at the inverse function to f .

Note that when f has the same value for more than one argument, you must decide which of these arguments you want to call the value of the inverse function.

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