Which function has an inverse that is also a function? A. {(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)}
B. {(-4, 6), (-2, 2), 6-1, 6), (4, 2), (11, 2)}
C. {(-4,5), (-2, 9), (–1, 8), (4, 8), (11,4)}
D. {(-4, 4), (-2, -1), (–1, 0). (4.1), (11, 1)}

Given:

The different functions in the form of set of ordered pairs.

To find:

The function which has an inverse that is also a function.

Solution:

A relation is a function if there exists unique y-value for each x-value.

We know that the inverse transformation is defined as:

So, the inverse of function is also a function if their exists unique x-value for each y-value in the function.

In option A, all x-values and y-values are unique. It means, inverse of this function is also a function. So, option A is correct.

In option B, and when . It means, inverse of this function is not a function. So, option B is incorrect.

In option C, and when . It means, inverse of this function is not a function. So, option C is incorrect.

In option D, and when . It means, inverse of this function is not a function. So, option D is incorrect.

Therefore, the correct option is A.

The students bought 16 azaleas plants.

Step-by-step explanation:

Given that:

Total plants bought by student council = 36

Cost of each azaleas plant = $6

Cost of each lily plant = $5

Total amount spent = $196

Let,

x be the number of azaleas

y be the number of lilies

x+y = 36       Eqn 1

6x+5y=196     Eqn 2

Multiplying Eqn 1 by 6

6(x+y=36)

6x+6y=216      Eqn 3

Subtracting Eqn 2 from Eqn 3

(6x+6y)-(6x+5y)=216-196

6x+6y-6x-5y=20

y=20

Putting y=20 in Eqn 1

x+20=36

x=36-20

x=16

Hence,

The students bought 16 azaleas plants.