No They have no special significance All of these are simply used by convention to refer to a function For example, f(x)=e^x, a(x)=e^x, and z(x)=e^x all mean the same thing However, some notations mean only one thing For example, zeta(s) refers to the Riemann zeta function sum_(n=1)^oo1/n^s (See this link for more info Riemann zeta function) In general,Thus, f first translates x into I, if it is outside I, and otherwise, untranslates and computes g, if it is in I It follows that f (f (x)) = g (x) for all x outside I There are 2 R many such h's, and hence also this many f'sQED If g is continuous, then this f can be chosen also to be continuousF(x) = x 3 g(x) = x 5 defined for all real numbers (Note composite functions may have a different notation such as (f g)(x)) Q1) Solve the equation fg(x) = 27 Firstly, we must find the composite function fg(x) in terms of x before we solve it In order to do this, we can break down the function in the following way fg(x) = fg(x) = f(x5)
Composition Of Functions Composing Functions At Points
