How to do Multiplication of function by a scalar ? Explain it by giving example

Explanation

What is Multiplication of a Function by a scalar?

Function happens to be a correspondence f between elements of a space X and those of a space Y such that any element x of X has a unique corresponding element y of Y which is denoted y=f(x). The following is a widely used shorthand for "a function f from X to Y "

 f:X→Y.   

In most cases f(x) is defined for all x∈X, but sometimes its domain of definition is smaller. The reason to allow such aberration is that most of the elementary functions are real (X=R) and real-valued (Y=R) and are defined by some kind of formulas. E.g., f(x)=x2−10. However, some formulas are not defined for all real values as, for example, f(x)=1/(x−1) which is not defined for x=1. The right way to described this latter function is (−∞,1)∪(1,∞)→R. Thus we often write 1/(x−1):R→R and try not to forget that x=1 is an exceptional point that does not belong to the domain of definition of that function.

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