Step-by-Step Strategies for Functions and Inequalities in CAT Quant Section
The basic strategy to solve questions on Functions and Inequalities in CAT Quant Section is to first check the domain. For functions always look for symmetry form while for inequalities use the number line test.
In the CAT exam, usually questions from Functions and Inequalities are usually integrated with topics like quadratic equations, modulus, relations, differentiation. With respect to questions in CAT Functions and Inequalities from Quant Section it is important to start with domain analysis and thereby classify the function whether it is linear, quadratic or modulus. Moreover for the inequalities section it is important to express the inequality in the standard form and isolate the variable on the one side of the equation. In this article we have systematically highlighted on how to solve these questions correctly in the CAT exam.
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Step-by-Step Strategy for Functions
Aspirants can follow the steps to solve the questions on functions.
Steps | Details |
|---|---|
Understand the Question | Take note that the domain of the function is the valid input while the range is the possible output |
Check Domain of Function | In order to check domain restrict the value to
|
Next Find Range | To find range follow the transformation method by using Quadratic, Rational and Composition techniques |
Use Graphical Representation | Rough sketches help with symmetry (odd/even functions), increasing/decreasing behavior, and boundary values. |
For Functions, candidates must take note that
- Use Substitution Method for options
- f(x+y) = f(x)+f(y) → linear function
- Modulus Function - Split two cases
Also Read: Effective Guessing Strategies for CAT Verbal Ability
Step-by-Step Strategy for Inequalities
Aspirants can follow the steps to solve the questions on inequalities
Steps | Details |
|---|---|
Simplify Expression | Factorise the quadratic equation. Bring the values to one side |
Use Number Line Method |
|
Absolute Value | Split into cases based on sign |
Exponential / Logarithmic |
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For Inequalities, candidates must take note that
- Use symmetry (e.g., |x| ≥ k always gives two branches).
- Eliminate wrong options quickly with test values.
- For equation ax² + bx + c > 0 → solution lies outside roots if a > 0.
- For equation ax² + bx + c < 0 → solution lies between roots if a > 0.
Also Read: Caselets vs Graphs in CAT DILR and How to Choose
Tricks to Solve Functions in CAT
Applicants can follow the methods to solve Functions in CAT exam.
Method | Detailed Steps |
|---|---|
Substitution Method |
Tip: If f(x) = x2+1 then f(f(x)) = f(x2+1) = (x2+1)2+1. |
Use Graph Visualization | Replace f(x)=∣g(x)∣ with cases
|
Piecewise Functions | For modulus or floor functions, break into intervals Example: f(x) = ∣x−2∣ Case 1 - x ≥ 2 → f(x) = x−2 Case 2 - x < 2 → f(x) = - (x - 2) = 2 - x |
Tricks to Solve Inequalities in CAT
Applicants can follow the methods to solve Functions in CAT exam.
Methods | Tricks |
|---|---|
Tricks for Linear Inequalities | Solve like equations, but flip the inequality sign when multiplying/dividing by a negative number. For example- -2x > 6 ⟹ x < –3 |
Tricks for Quadratic Inequalities |
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Tricks for Rational Inequalities |
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