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).

24

step-by-step explanation:

if it takes 8 pounds to make 12 divide 12 by 8 and you get 1.5, 1.5 x 16 = 24

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3