Question

Evaluate the function rule for the given value \[f\left( x \right)=5x\] for \[x=2\] .

Answer 1

Hint: For solving this problem, we should implement the concept of mapping and functions. We should understand the fact that the function maps from x to y and the mapping is “multiplication by $5$ “. Knowing this, we can write the rule for \[x=2\] .

Complete step by step answer:
Mapping is any prescribed way of assigning to each object in one set a particular object in another (or the same) set. Mapping applies to any set: a collection of objects, such as all whole numbers, all the points on a line, or all those inside a circle. For example, “multiply by three” defines a mapping of the set of all whole numbers onto the set of even numbers. In mathematics, the words mapping, map, and transformation tend to be used interchangeably. The set which is mapped is called the domain and the set onto which the mapping is done is called the range.
Now, we can call a mapping to be a function only if each element of the domain has only one image in the range and that must be unique. In this problem, we are given that the function is \[y=f\left( x \right)=5x\] . It is read as “f is a function which maps from x to y”. The mapping is “multiplication by $5$ “. So, for the value of \[x=2\] , we can write the function rule as,
\[f\left( 2 \right)=5\left( 2 \right)=5\times 2=10\]
Thus, we can conclude that the function rule for the given value \[f\left( x \right)=5x\] for \[x=2\] is \[f\left( 2 \right)=5\left( 2 \right)=5\times 2=10\] .

Note: For these problems, we must know the basics of relations, mappings and functions. We always tend to ignore these topics in our syllabus, but they form the foundation of modern day mathematics.