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1.4 Standard functions

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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 argument of one function as value of another, and taking the “inverse”.
Most of the functions we encounter will be standard functions.
Examples: 4x2, x sin(x), exp(sin(x)) / x.



Exercises 1.7 For what values can you define the inverse of the function cos(sin(x)). Hint: set f = cos(sin(x)) look at its inverse and figure out the answer. Solution