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CAT Modulus inequalities - Practice Questions & MCQ

Edited By admin | Updated on Oct 04, 2023 04:20 PM | #CAT

Concepts Covered - 1

Modulus inequalities

Introduction to Functions

Definition:

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. The set of inputs is called the domain and the set of possible outputs is called the codomain.

Notation:

A function f from set A to set B is denoted by f: A B.

Example:

Consider a function f defined as $\mathrm{ f(x) = x^{2}}$ . Here, for each value of x , we get a unique value of f(x) . If x = 2 , then f(2) = 4 .

Foundation Building Questions:

Question 1:

Given a function f: $\mathrm{R \rightarrow R}$ defined as $\mathrm{f(x) = x^{2} + 2x + 5 }$ . Find the value of f(3).

Solution:

Plug in the value x = 3 into the function.

$\mathrm{f(3) = 3^{2}+ 2(3) + 5 = 9 + 6 + 5 = 20 }$

Question 2:

If a function $\mathrm{g:R\rightarrow R }$ is defined as $\mathrm{g(x) = 3x - 7}$ , what is the value of $\mathrm{g(4)}$ ?

Solution:

Substitute x = 4 into the function.

$\mathrm{g(4) = 3(4) - 7 = 12 - 7 = 5 }$

Tips and Tricks related to 'Introduction to Functions':

1. Understanding Domain and Codomain:

- Always remember that the domain is the set of all possible input values, while the codomain is the set of all possible outputs. Not every value in the codomain needs to be an output for some input.

2. Substitution is Key:

- For basic functions, substitution is the quickest way to evaluate the function. For instance, to find f(2) for $\mathrm{ f(x) = x^{2}+ 3x }$ , simply replace every x with 2.

3. Visual Representation:

- Drawing a quick sketch of the function can often provide insights, especially when understanding the behaviour of the function across its domain.

4. Consistent Outputs:

- Ensure that for each input, there's only one corresponding output. If there are multiple outputs for a single input, it's not a function.

This is a concise introduction to the concept of functions for students preparing for management entrance exams. Remember, consistent practice and understanding the basic concepts deeply is the key to mastering functions.