Question

If f(1)=2f(1)=2 and f(n)=f(n-1)^2-n then find the value of f(4)

Answer 1

Given that $f(1)=2$ and $f(n)=[f(n-1)]^2-n$

We need to determine the value of f(4)

To determine the value of f(4), we need to know the values of the previous terms f(2), f(3).

The value of f(2):

The value of f(2) can be determined by substituting n = 2 in the function $f(n)=[f(n-1)]^2-n$

Thus, we get;

$f(2)=[f(2-1)]^2-2$

$f(2)=[f(1)]^2-2$

$f(2)=2^2-2$

$f(2)=2$

Thus, the value of f(2) is 2.

The value of f(3):

The value of f(3) can be determined by substituting n = 3 in the function $f(n)=[f(n-1)]^2-n$

Thus, we get;

$f(3)=[f(3-1)]^2-3$

$f(3)=[f(2)]^2-3$

$f(3)=2^2-3$

$f(3)=1$

Thus, the value of f(3) is 1.

The value of f(4):

The value of f(4) can be determined by substituting n = 4 in the function $f(n)=[f(n-1)]^2-n$

Thus, we get;

$f(4)=[f(4-1)]^2-4$

$f(4)=[f(3)]^2-4$

$f(4)=1^2-4$

$f(4)=-3$

Thus, the value of f(4) is -3.