Question

Which table represents the inverse of the function defined above? theres an attatchment

Answer 1

Answer:

Table B represents the inverse of the function.

Step-by-step explanation:

Let us take any two points from the given table of the original function and they are (0,5) and (2,11).

Therefore, the linear equation that is satisfied by those two points will be given by  

$\frac{y - 11}{11 - 5} = \frac{x - 2}{2 - 0}$

⇒ y - 11 = 3(x - 2)

⇒ y - 11 = 3x - 6

⇒ y = 3x + 5

Therefore, the original function is f(x) = y = 3x + 5 ......... (1)

Now, rearranging the function we get 3x = y - 5

⇒ $x = \frac{1}{3}(y - 5)$

Therefore, the inverse function of f(x) is $g(x) = y = \frac{1}{3}(x - 5)$ ........ (2)

Now, the points on the table given in option B are (-1,-2), (5,0), (11,2) and (17,4) all satisfy the inverse equation (2).

Therefore, table B represents the inverse of the function. (Answer)