Question

Determine whether each of these functions from {a, b, c, d} to itself is one-to-one.

Answer 1

Answer:

Only function (a) is one-to-one.

Step-by-step explanation:

If every element of the range of the function corresponds to exactly one element of the domain, then the function is called one-to-one.

The elements of a function are

A = {a,b,c,d}

We need to check whether $f\rightarrow A\times A$ is one to one or not.

(a)

f (a) = b, f (b) = a, f (c) = c, f (d) = d

Here, for each value of x, there exist exactly one value of y.

Therefore, this function is one-to-one.

(b)

f (a) = b, f (b) = b, f (c) = d, f (d) = c

Here, the value of function is b for x=a and x=b. For two domains the functions has same range.

Therefore, this function is not one-to-one.

(c)

f (a) = d, f (b) = b, f (c) = c, f (d) = d

Here, the value of function is d for x=a and x=d. For two domains the functions has same range.

Therefore, this function is not one-to-one.