Functions Chapter in mathematics is quite important for JEE Preparation. Fundamentals of this chapter is required to clear to move ahead.I am trying to give few Important Solved Functions problems for JEE Maths in this article .

You can refer below link for below for the detailed study material on Relations and Function

Relation and function Study material

So Here we go.I hope you will like it

**Question 1**

If 1 lies between the roots of equation and denote the greatest integer’s value of , then find the value of

**Solution**

Let f(x) =

Since 1 lies between the roots

(1)

This implies that

Now we know that Arithmetic Mean between two number is always greater than or equal to the Geometric mean

So choosing two number as and 16

(2)

Hence as per definition of function [x]

**Question 2**

Find the number of real roots of

**Solution**

Let

(3)

Clearly has only the real root

This implies that has a local minima of negative value.

has a local minima and local maxima

This implies that has three real roots.

**Question 3**

If and be periodic and non-periodic functions respectively, then is

(a) always periodic

(b) never periodic

(c) periodic, when is a linear function of

(d) can’t say

**Solution**

(c) Since we know if is periodic then is also periodic function. Hence should be linear function of .

**Question 4**

Let and be bijective functions where and respectively. The number of elements in the range set of is

(a) 1

(b) 2

(c) 3

(d) 4

**Solution**

(b) Range of for which is defined is

Hence domain of has two elements.

Therefore range of also has two elements.

**Question 5**

Domain and Range of is respectively, where denotes the greatest integer function.

(a)

(b)

(c)

(d)

**Solution** (a)

is defined when as, when ;

Range of is