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vlada-n [284]
3 years ago
6

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

f(a) = b, f(b) = b, f(c)=d, f(d) = c. c) f(a) = d, f(b) = b, f(c)=c, f(d) = d.
Mathematics
1 answer:
vfiekz [6]3 years ago
8 0

Answer:

The first one is one-to-one.

The second one is not one-to-one.

Third one is not one-to-one.

The problem:

Are the following one-to-one from {a,b,c,d} to {a,b,c,d}:

a)

f(a)=b

f(b)=a

f(c)=c

f(d)=d

b)

f(a)=b

f(b)=b

f(c)=d

f(d)=c

c)

f(a)=d

f(b)=b

f(c)=c

f(d)=d

Step-by-step explanation:

One-to-one means that a y cannot be hit more than once, but all the y's from the range must be hit.

So the first one is one-to-one because:

f(a)=b

f(b)=a

f(c)=c

f(d)=d

All the elements that got hit are in {a,b,c,d} and all of them were hit.

The second one is not one-to-one.

The reason is because f(a) and f(b) both are b.

Third one is not one-to-one.

The reason is because f(a) and f(d) are both d.

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Answer:

Step-by-step explanation:

As 4 is accumulated by thousands place

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The no is

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Marizza181 [45]

Answer:

Correct answer:  x₁ = 1 / √3 = √3 / 3  or  x₂ = - 1 / √3 = - √3 / 3

Step-by-step explanation:

Given:

3 x⁴ + 14 x² - 5 = 0   biquadratic equation

this equation is solved by a shift  x² = t and get:

3 t² + 14 t - 5 = 0

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Lyrx [107]

Answer:

3(4+x)

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