8.1. Suppose f(x) = 6x – 2 is the encoding function.
I don't mind helping wit an answer, but I resent being asked to provide the question as well.
It seems like you have provided an equation for a function, where f(x) represents the output of the function for a given input x. The given encoding function is f(x) = 6x – 2.
To understand this encoding function, let's break it down:
1. The function is linear: The equation is in the form of y = mx + c, where m represents the slope of the line and c represents the y-intercept. In this case, the slope (m) is 6, and the y-intercept (c) is -2.
2. Encoding input (x) to output (f(x)): To use this encoding function, you can plug in a value for x, and the function will output the corresponding value for f(x). For example, if you want to encode the value x = 4, you would substitute it into the equation: f(4) = 6(4) - 2 = 24 - 2 = 22. Therefore, the encoding of 4 using this function is 22.
3. Decoding output (f(x)) to input (x): If you are given an output value from the function (f(x)), and you want to find the corresponding input value (x), you can rearrange the equation. In this case, the equation is f(x) = 6x - 2. So, if you are given f(x) = 34, you can solve for x as follows: 34 = 6x - 2. Adding 2 to both sides gives you 36 = 6x. Dividing by 6, you get x = 6. Therefore, the decoding of 34 using this function is 6.
So, the encoding function f(x) = 6x - 2 allows you to encode an input value to an output value and decode an output value to its corresponding input value using the given equation.