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.
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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