Question

Helppp!! I NEED HELP PLEASE

Answer 1

Given:

The table of values for the function f(x).

To find:

The values
`f^(-1)(f(3.14))` and
`f(f(-7))`.

Solution:

From the given table, it is clear that the function f(x) is defined as:

`f(x)=\{(-14,11),(-7,-12),(-12,-5),(9,1),(10,-2),(-2,13)\}`

We know that if (a,b) is in the function f(x), then (b,a) must be in the function
`f^(-1)(x)`. So, the inverse function is defined as:

`f^(-1)(x)=\{(11,-14),(-12,-7),(-5,-12),(1,9),(-2,10),(13,-2)\}`

And,

`f^(-1)(f(a))=f^(1)(b)`

`f^(-1)(f(a))=a` ...(i)

Using (i), we get

`f^(-1)(f(3.14))=3.14`

Now,

`f(f(-7))=f(-12)`

`f(f(-7))=5`

Therefore, the required values are
`f^(-1)(f(3.14))=3.14` and
`f(f(-7))=5`.