Given:
The function is [tex]f(f(x))=x^2-1[/tex].
To find:
The value of f(f(f(f(3)))).
Solution:
We have,
[tex]f(f(x))=x^2-1[/tex]
Now,
[tex]f(f(f(f(x)))=(f(f(x)))^2-1[/tex]
[tex]f(f(f(f(x)))=(x^2-1)^2-1[/tex]
Putting x=3, we get
[tex]f(f(f(f(3)))=((3)^2-1)^2-1[/tex]
[tex]f(f(f(f(3)))=(9-1)^2-1[/tex]
[tex]f(f(f(f(3)))=(8)^2-1[/tex]
[tex]f(f(f(f(3)))=64-1[/tex]
[tex]f(f(f(f(3)))=63[/tex]
Therefore, the value of f(f(f(f(3)))) is 63.
