CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

The question is about two functions. We need to find out the value of p - q which is given in two functions. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 8: If f(x – 3) = 2x³ + p – qx and f(x² – 4) = x² – 8q + 6p, then what is the value of p – q?

1. 5
2. 10
3. 6
4. Cannot determine

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Functions: The concept of equating f(0) of a function given two instances of the function.

f(x – 3) = 2x³ + p – qx
Let x = 3, then f(0) = 54 + p – 3q ---- (1)
f(x² – 4) = x² – 8q + 6p
Let x² = 4, then f(0) = 4 – 8q + 6p --- (2)

From (1) and (2)
54 + p – 3q = 4 – 8q + 6p
50 = 5p – 5q
p - q = 10

The question is "If f(x – 3) = 2x³ + p – qx and f(x² – 4) = x² – 8q + 6p, then what is the value of p – q?"

Hence the answer is "10"

Choice B is the correct answer.