LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RELATION & FUNCTION - FURTHER DISCUSSION ON DOMAIN OF A FUNCTION

**Further Discussion On The Domain Of A Function –**

**Consider the following
functions.**

** 1**

**1.) The function ------
has no meaning when x = 0, so this function is **

** x**

**defined for all real numbers except 0.**

**2.) The function √x is
defined for only the non-negative real numbers.**

**3.) Since a negative number
does not have a real square root, therefore, the function √x(8 – x).**

**Is defined only when x(8 –
x) ≥ 0.**

**This will be true only when both the factors x
and (8 – x) are greater than or equal to 0.**

**If, x ≥
0 and (8 – x) ≥ 0, then 0 ≤ x ≤ 8.**

**The alternative x ≤ 0 and (8 – x) ≤ 0, is impossible because
(8 – x) ≤ 0 => 8 ≤ x
=> x ≥ 8.**

**We can’t have x ≤ 0 and x ≥ 8 at the same time.
So the function √x(8 – x) is defined only if
0 ≤ x ≤ 8.**

__Definition –__ The set of numbers
x for which function f(x) is defined is called the domain of the function.

**Thus, the domain of the function f(x) = √x(8 –
x) is the set of real numbers such that 0 ≤ x ≤ 8. These are any number for which √x(8 – x) exists.**