Chapter 5, Problem 13RE

(a)

To determine

To verify : The given function one to one.

Explanation of Solution

Given: The functions is $\left\{\left(1,2\right),\left(3,5\right),\left(5,8\right),\left(6,10\right)\right\}$

The domain of the function is $\left\{1,3,5,6\right\}$ .

The range of the function is $\left\{2,5,8,10\right\}$ .

On observing the range of the function, no element in the range repeats its value.

Hence, the function is one to one.

(b)

To determine

To find : The inverse of the given function.

Explanation of Solution

Given: The functions is $\left\{\left(1,2\right),\left(3,5\right),\left(5,8\right),\left(6,10\right)\right\}$

The domain of the function is $\left\{1,3,5,6\right\}$ .

The range of the function is $\left\{2,5,8,10\right\}$ .

If the range is made as domain of another function, then the new function will be the inverse of the previous function.

So, the inverse of the function is,

  $\left\{\left(2,1\right),\left(5,3\right),\left(8,5\right),\left(10,6\right)\right\}$

Therefore, the inverse of the function is $\left\{\left(2,1\right),\left(5,3\right),\left(8,5\right),\left(10,6\right)\right\}$ .