MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 440 off
USE CODE: MOB20

Increasing or decreasing function

The function f is said to be an increasing function in its domain D if

        ∀ x2 > x1 => f(x2) > f(x1); x1, x2 ε D       

increasing-function                                

However if

strictly-increasing-function
        ∀ x2 > x1 => f(x2) > f(x1), x1, x2 ε D       
         

The function 'f' is said to be strictly increasing

The function 'f' is said to be decreasing function in its domain D if

        ∀ x2 > x1 => f(x2) < f(x1); x1, x2 ε D                
decreasing-function 

However if

        ∀ x2 > x1 => f(x2) < f(x1); x1, x2 ε D
strictly-decreasing-function 

Then it said to be strictly decreasing.

Strictly increasing and decreasing functions are also called Monotonic Function.

Illustration:

        Is y = 2x + 3 increasing/decreasing function.

Solution:

Since, ∀ x ε R, y ε R

        Therefore Df = R

Let x2 > x1; x1, x2 ε R

        =>     2x2 > 2x1

        =>     2x2 + 3 > 2x1 + 3

        =>     f(x2) > f(x1)

        =>     y = f(x) = 2x + 3 is strictly increasing function.

Examples:

1. Are the following function increasing/decreasing?

        (a)    y = x3 + 8                 (b)    y = -2x + 4
Ans.  (a) Decreasing

        (b) Strictly decreasing 

You can participate in the online tests conducted by askIITians and also give answers in AQAD (A Question  A Day) just by visiting the website askIITians.com. This will give you a number of benefits in the online live classroom courses targeting IIT JEE 2010 and 2011. Read online Study material for IIT JEE and AIEEE preparation absolutely free at askIITians.com.

To read more, Buy study materials of Set Relations and Functions comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 4,500 off
USE CODE: Venkat30