PLEASEEWW HELPPP WILL MARK BRAINLIESTTT

Could the inverse of a non-function be a function? Explain or give an example.

Kitty [74]

Answer:

The inverse of a non-function mapping is not necessarily a function.

For example, the inverse of the non-function mapping $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ is the same as itself (and thus isn't a function, either.)

Step-by-step explanation:

A mapping is a set of pairs of the form $(a,\, b)$ . The first entry of each pair is the value of the input. The second entry of the pair would be the value of the output.

A mapping is a function if and only if for each possible input value $x$ , at most one of the distinct pairs includes $x\!$ as the value of first entry.

For example, the mapping $\lbrace (0,\, 0),\, (1,\, 0) \rbrace$ is a function. However, the mapping $\lbrace (0,\, 0),\, (1,\, 0),\, (1,\, 1) \rbrace$ isn't a function since more than one of the distinct pairs in this mapping include $1$ as the value of the first entry.

The inverse of a mapping is obtained by interchanging the two entries of each of the pairs. For example, the inverse of the mapping $\lbrace (a_{1},\, b_{1}),\, (a_{2},\, b_{2})\rbrace$ is the mapping $\lbrace (b_{1},\, a_{1}),\, (b_{2},\, a_{2})\rbrace$ .

Consider mapping $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ . This mapping isn't a function since the input value $0$ is the first entry of more than one of the pairs.

Invert $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ as follows:

$(0,\, 0)$ becomes $(0,\, 0)$ .
$(0,\, 1)$ becomes $(1,\, 0)$ .
$(1,\, 0)$ becomes $(0,\, 1)$ .
$(1,\, 1)$ becomes $(1,\, 1)$ .

In other words, the inverse of the mapping $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ would be $\lbrace (0,\, 0),\, (1,\, 0),\, (0,\, 1),\, (1,\, 1) \rbrace\!$ , which is the same as the original mapping. (Mappings are sets. There is no order between entries within a mapping.)

Thus, $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ is an example of a non-function mapping that is still not a function.

More generally, the inverse of non-trivial ellipses (a class of continuous non-function $\mathbb{R} \to \mathbb{R}$ mappings, including circles) are also non-function mappings.

3 0

2 years ago

Type your answer in the box. You may use numbers, a decimal point (.), and/or a negative sign (-) in your answer. Stella is rent

True [87]

420 blaze it

420 miles

5 0

3 years ago

you know that the sum of -5 and another integer is a positive integer.what can you conclude about the sign of the other integer?

denis-greek [22]

-5 + x = +

adding/subtracting numbers with same/different signs : if the signs are the same, whether both negative or positive, then the answer will contain the same sign.
Example : -2 + (-2) = -2-2 = -4 : both signs are negative, the sign stays negative.
5 + 5 = 10 : both signs are positive, the sign stays positive.
However, if the signs are different, u subtract the smallest number from the largest number and take the sign of the larger number.
Example : -2 + 5 = 3...I took 5 - 2..which is 3, and took the sign of the largest number (+)...so the answer is 3.
-5 + 2 = -3....I took 5 - 2 and got 3, but used the larger number sign (-) making the answer -3.

now for ur question....u can conclude that the sign of the other integer would have to be positive. As for the value, in order for the answer to be positive, the integer would have to be larger then + 5.
Example :
-5 + 6 = 1
-5 + 7 = 2
if u picked a positive number smaller then 5...
-5 + 4 = -1
-5 + 3 = -2
u would not get a positive result.

7 0

3 years ago

Read 2 more answers

The area of a rectangle is 18 m² if the length is 6 m less than five times the width then find the dimensions of the rectangle r

oksano4ka [1.4K]

Answer:

Step-by-step explanation:

width = w

L = 5w - 6

w(5w - 6) = 18

5w^2 - 6w = 18

5w^2 - 6w - 18 = 0

Using the quadratic equation formula

x = 2.58997 and

x = -1.38997 This root cannot be. (No rectangle has a minus length.

w = 2.58997

L = 5*2.58997 - 6

L = 6.94985

w = 2.59

L = 6.95

3 0

3 years ago

JKL has vertices J(3, -5) K(-8, -1) and L(5,1). JKL will be reflected across the line y= -1 to form J'K'L'. Which quadrant will

katen-ka-za [31]

Answer:

The correct answer is second quadrant.

Step-by-step explanation:

Vertices of J ≡ (3 , -5) which shows J is in fourth quadrant. When J is reflected across the line y = -1, the point J moves to first quadrant as J' with coordinates (3 , 3).

Vertices of K ≡ (-8 , -1) which shows K is in third quadrant. When K is reflected across the line y = -1, the point K remains where it is (in the third quadrant) as it is on the line y = -1 only.

Vertices of L ≡ (5 , 1) which shows L is in first quadrant. When L is reflected across the line y = -1, the point L moves to fourth quadrant as L' with coordinates (5 , -3).

Thus each of the first, fourth and third quadrant contains a vertex except the second quadrant.

4 0

3 years ago