CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

The question is about range of function. This one is simple, we just need to find out the range of a quadratic equation. Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.

Question 16: Find range of f(x) = x² – 6x + 14?

1. (-∞, 8)
2. (-∞, 100)
3. (-∞, 45)
4. (5, ∞)

Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : Range is the set of values taken by the function

x² - |x + 3| + x > 0
Given, f(x) = x² – 6x + 14
f(x) can be written as x² – 6x +9 -9 + 14
=> f(x)= (x-3)² + 5
As you can see, for whatever value of x, the term (x-3)² is always positive. The least value it can take is zero, so the minimum value of the function is 5.
The maximum value can range until infinity.
Therefore, Range = (5, ∞)

The question is "Find range of f(x) = x² – 6x + 14?"

Hence the answer is "(5, ∞)"

Choice D is the correct answer.