Mathematics, 22.09.2019 05:10 ayoismeisalex

Which function has an inverse that is also a function? {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} {(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)} {(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)} {(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}

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Answer from: IIIKiXIII

First Option $\{(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)\}$

Step-by-step explanation:

A relation is a function if and only if each value of the set "domain" has assigned only one value in the set "range".

That is, there is an output value and for each input value x.

Then the inverse of a function f (x) is denoted $f ^ {- 1} (x)$ and the domain of this function is the range of the function f (x) . Similarly, the range of $f ^ {- 1} (x)$ is the domain of f (x) .

That is, if f (x) contains the points $\{(1, 3) (4, 9) (8, 17)\}$ Then $f ^ {- 1} (x)$ contains the points $\{(3, 1) (9, 4) (17, 8)\}$ .

So if the inverse of a function f (x) is also a function then f (x) must be a "one-to-one" function. This means that there can not be an equal value of y assigned to two different values of x.

For example $f (x) = \{(1, 4) (-1, 4) (1, 6) (-2, 6)\}$

f (x) is a function, but $f ^ {- 1} (x)$ is not a function.

To solve this problem, identify only the set of ordered pairs that is "one-to-one"

{(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} It is a "one-to-one" function

{(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)} It is not a "one-to-one" function

{(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)} It is not a "one-to-one" function

{(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)} It is not a "one-to-one" function

Only the inverse of $f (x) =\{(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)\}$ is a function

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is