Given that
and
![f(n)=[f(n-1)]^2-n](https://img.qammunity.org/2021/formulas/mathematics/high-school/g2x7udl29g9mwyh53fsjgopohr6kqq64hr.png)
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](https://img.qammunity.org/2021/formulas/mathematics/high-school/g2x7udl29g9mwyh53fsjgopohr6kqq64hr.png)
Thus, we get;
![f(2)=[f(2-1)]^2-2](https://img.qammunity.org/2021/formulas/mathematics/high-school/utd1fs2ajzu3fphofg13rguvmeopsv78hq.png)
![f(2)=[f(1)]^2-2](https://img.qammunity.org/2021/formulas/mathematics/high-school/mjk28krynendyy551yl04buk66kezbtavs.png)


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](https://img.qammunity.org/2021/formulas/mathematics/high-school/g2x7udl29g9mwyh53fsjgopohr6kqq64hr.png)
Thus, we get;
![f(3)=[f(3-1)]^2-3](https://img.qammunity.org/2021/formulas/mathematics/high-school/n66wwetefs2q4vy4zshglko35tai6uvds2.png)
![f(3)=[f(2)]^2-3](https://img.qammunity.org/2021/formulas/mathematics/high-school/ywa6elzw90nw8plux5lkkpv7a8arnlwxes.png)


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](https://img.qammunity.org/2021/formulas/mathematics/high-school/g2x7udl29g9mwyh53fsjgopohr6kqq64hr.png)
Thus, we get;
![f(4)=[f(4-1)]^2-4](https://img.qammunity.org/2021/formulas/mathematics/high-school/s4jrhjuyzekmjckknsyznzgdpvfx3ylbpd.png)
![f(4)=[f(3)]^2-4](https://img.qammunity.org/2021/formulas/mathematics/high-school/jihfmzssf0mulxbp5h3dlkmn2kgt9jwivr.png)


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