Determine whether each of these functions from z to z is one-to-one. a) f(n) = n - 1 b) f(n) = n2 + 1 c) f(n) = nº d) f(n) = [n/2]

 The correct option is

(a) f(n) = n - 1.

Step-by-step explanation:  We are given to determine whether the given functions are one-to-one or not.

We know that a function y = f(x) is one-to-one if and only if

f(x) = f(y)  ⇔  x = y.

That is, any two distinct elements cannot have the same image.

(a) The given function is

Let us consider that

Similarly,

So, this function is one-to-one.

(b) The given function is

Let us consider that

That is, there may be two unequal elements having same image.

For example, f(-1)=(-1)²+1=1+1=2,  f(1)=(1)²+1=1+1=2.

It implies that f(-1)=f(1) but 1 ≠ -1.

So, the given function is not one-to-one.

(c) The given function is

Here, the image of all the elements is 1.

For example,

f(2)=f(3)  but  2≠3.

So, more than one element is having the same image and so the function cannot be one-to-one.

(d) The given function is

Here, we see that

So, f(2)=f(3) but 2≠3.

So, the given function is not one-to-one.

Thus, the correct option is (a).

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

step-by-step explanation:

your mom