a cube length has a side length of 7 meters. A smaller cube with side length 3.5 has been cut out of the larger cube

Mathematics

1 answer:

SOVA2 [1]3 years ago

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Determine whether each of these functions from {a, b, c, d} to itself is one-to-one, onto, bijective. (a) f(a)=b, f(b)=a, f(c)=c

Monica [59]

Answer:

See below

Step-by-step explanation:

Let S={a,b,c,d}. f : S→S is 1-1, if different elements of S have different images respect to f. f is onto if f(S)={f(x)|x∈S}=S. f is bijective if f is 1-1 and onto.

a) f is 1-1. Indeed, each element of S has a different image respect to f, thus no different elements of S have the same image (f(x)≠f(y) if x≠y).

f is onto, because f(S)={f(a),f(b),f(c),f(d)}={b,a,c,d}={a,b,c,d}=S. Then the direct image of f is equal to the codomain S, hence f is onto.

f is 1-1 and onto, hence f is bijective.

b) f is not 1-1. a≠b but f(a)=b=f(b).

f is not onto. a∈S, but there is not element x such that f(x)=a. In other words, the direct image f(S)={f(a),f(b),f(c),f(d)}={b,b,c,d}={b,c,d} is not equal to S.

f is not bijective, since f is not 1-1.

c) f is not 1-1. a≠d but f(a)=d=f(d).

f is not onto. a∈S, but there is not element x such that f(x)=a. In other words, the direct image f(S)={f(a),f(b),f(c),f(d)}={d,b,c,d}={b,c,d} is not equal to S.

f is not bijective, since f is not onto.

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3 years ago

Write 3.19 as a ratio of two integers.<br><br><br> Enter your answer as a reduced improper fraction

grin007 [14]

Answer:

319/100

Hope this helps!

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Find the value of x for which abcd must be a parallelogram 3x 4x-5

Aliun [14]

Let's first denote the intersection point of diagonals with O. In this parallelogram, we can observe that ΔAOB is congruent to ΔCOD because of AB=CD and the angles ∠BAO and ∠OCD are equal (They are alternate angles). According to the rule of congruency, 3x=4x-5 and x=5

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3 years ago

given f(x)=4x-1, find the domain value if the range value is -5 given f(x)=4x-1, find the domain value if the range value is -5

olga55 [171]

the domain is -1. Let 4x-1=-5 then solve

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3 years ago

A person driving along the road moves at a rate of 56 mph driven. How far does the person driving 1.5 hours? Show the calculatio

levacccp [35]

Greetings!

We can find out how many miles driven in 1.5 hours buying creating a simple expression:
$56*1.5$
Evaluate:
$=84$

In 1.5 hours, the person would've driven 84mph.

Hope this helps.
-Benjamin

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4 years ago