Discussion

Explanation:

Given function can be rearranged as,

f(x) – f(x – 1) = 2x

⇒ f(2) – f(1) = 2 × 2
⇒ f(3) – f(2) = 2 × 3
⇒ f(4) – f(3) = 2 × 4

⇒ f(31) – f(30) = 2 × 31

Adding all these equations we get

f(31) – f(1) = 2 × (2 + 3 + 4 + … + 31)

f(31) – 1 = 2 × ((31×32)/2-1) = 990

⇒ f(31) = 991

Alternately,
From the given function ;

f(2) = 4 + f(1) = 5 = 22 + 1

f(3) = 6 + f(2) = 6 + 5 = 11 = 32 +2

f(4) = 8 + f(3) = 8 + 11 = 19 = 42 + 3

Hence we can see that f(x) = x2 + (x-1)

Hence f(31) = 312 + 30 = 991.

Hence, option (d).

» Your doubt will be displayed only after approval.


Doubts


Feedback

Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.


© 2024 | All Rights Reserved | Apti4All