For each function below, determine whether or not the function is injective and whether or not the function is surjective. be sure to justify your answers.
(b) f: p({1,2,3}) + n given by f(a) = |a| (note: p(s) denotes the power set of a set s.)

The function is neither injective nor surjective

Step-by-step explanation:

f: P({1,2,3}) -> N is given by f(A) = |A|

where P(S) denotes the power set of a set S and |A| the number of elements of A

The function is not injective, for  

but  

The function is not surjective either, because 5 is a natural number which is not the image of any element A under f, i.e., there is no element in A in P({1,2,3}) such that f(A)=5

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb