Question

If f ( 1 ) = 2 f(1)=2 and f ( n ) = f ( n − 1 ) 2 − 5 f(n)=f(n−1) 2 −5 then find the value of f ( 4 ) f(4).

Answer 1

f(4) = 11

Explanation:

Given :

• base function ⇒ f(n) = f(n - 1)² - 5
• f(1) = 2

Solving :

• f(2) = f(1)² - 5
• f(2) = 2² - 5 = 4 - 5 = -1

• f(3) = f(2)² - 5
• f(3) = (-1)² - 5 = 1 - 5 = -4

• f(4) = f(3)² - 5
• f(4) = (-4)² - 5
• f(4) = 16 - 5 = 11

Answer 2

`f(1) = 2\\f(2)=f(2-1)^2-5=(f(1))^2-5 = 2^2-5 = -1\\f(3) = f(3-1)^2 - 5=f(2)^2-5=(-1)^2-5=-4\\f(4) = f(4-1)^2-5 = f(3)^2-5 = (-4)^2-5 = 11`

so f(4) = 11

Hope that helps!