In this question, we are asked to find the value of a function, i.e. f(10) with the help of the given conditions. Generally, the fundamentals are tested in such questions, so it is prudent to practice a lot of question from **CAT Functions and Algebra**. Historically, the CAT Exam is known for rolling out questions related to **Algebra** and **Functions**. From the **CAT Previous Year Paper, **we can infer that we can expect at least one question from this topic. Moreover, from the CAT Previous Year Paper, we see that the **CAT Exam** has ramped up the TITA-type questions and if you feel TITA questions are a little troublesome, solve this and practice more. For more TITA type questions, visit **CAT Question Paper**.

Question 3: If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals.

[TITA]

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Method of solving this CAT Question from Functions

Given, f(x+2) = f(x) + f(x+1) f(11) = 91, f(15) = 617

We get 91 + f(12) = f(13)

Let f(12) be equal to some value ‘a’

So, 91 + a = f(13).

f(12) + f(13) = f(14)

a + 91 + a = f(14)

So, f(14) = 2a + 91 f(13) + f(14) = 617

So, 91 + a + 2a + 91 = 617

3a + 182 = 617

a = 145

Substituting the value of a and f(11), we get

f(10)+ 91 = 145

f(10) = 54

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