Question

If f is a function such that f(f(x)) = x^2 - 1 what is f(f(f(f(3))))

Answer 1

Given:

The function is
`f(f(x))=x^2-1`.

To find:

The value of f(f(f(f(3)))).

Solution:

We have,

`f(f(x))=x^2-1`

Now,

`f(f(f(f(x)))=(f(f(x)))^2-1`

`f(f(f(f(x)))=(x^2-1)^2-1`

Putting x=3, we get

`f(f(f(f(3)))=((3)^2-1)^2-1`

`f(f(f(f(3)))=(9-1)^2-1`

`f(f(f(f(3)))=(8)^2-1`

`f(f(f(f(3)))=64-1`

`f(f(f(f(3)))=63`

Therefore, the value of f(f(f(f(3)))) is 63.