A function f:R→R defined by f(x)=2x is

The function f:R→R defined by f(x)=2x is a linear function. This function maps any real number x to the real number 2x.

Here are the steps to understand this function:

1. The domain of the function is all real numbers (R). This means that you can input any real number into the function.

2. The function is defined by the equation f(x)=2x. This means that to find the output of the function for a given input, you multiply the input by 2.

3. The range of the function is also all real numbers (R). This is because any real number multiplied by 2 is still a real number.

4. Therefore, this function takes any real number as input and outputs that number multiplied by 2.

5. This function is linear because the output increases proportionally with the input. In other words, if you graph this function, you will get a straight line.