Chapter 1.6, Problem 125E

(a)

To determine

To decode: The message by one to one function.

Answer to Problem 125E

The message is $\text{19 10 64 64 4 69 29 4 64 9 104 29 94}$

Explanation of Solution

Given data:

  $F(x)=2x-1$

Calculation:

We can write “Call me later” as $\text{ 3 1 12 12 0 13 5 0 12 1 20 5 18}$

So the equation for encoding the message is $F(x)=5x+4$

For encoding the message we have to put the digits of alphabet in f(x)

So the encoding message is:

  $\text{19 9 64 64 4 69 29 4 64 9 104 29 94}$

Conclusion:

The encoding message is $\text{19 10 64 64 4 69 29 4 64 9 104 29 94}$

(b)

To determine

To decode: The message by one to one function.

Answer to Problem 125E

The inverse function is $f^{-1}=\frac{x-4}{5}$ and message is “What Tire”.

Explanation of Solution

Given data:

  $F(x)=5x+4$

Calculation:

The inverse of function $F(x)=5x+4$:

So,

  $\begin{array}{l}y=5x+4\\ y-4=5x\\ \frac{y-4}{5}=x\\ f^{-1}(x)=\frac{x-4}{5}\end{array}$

The decoding function for message is $f^{-1}=\frac{x-4}{5}$

So the decode message for $\text{119 44 9 104 4 104 49 69 29}$ is

In digit: $23\text{ 8 1 20 0 20 9 13 5}$

Message: What Tire

Conclusion:

The inverse function is $f^{-1}=\frac{x-4}{5}$ and message is What Tire