Question

Find the domain of the function given by f(x) =1/rootx - modx

Answer 1

f(x) = 1/√{x - |x | }
for defining of function ,
x - | x | > 0
when, x > 0
x - x >0
0 > 0 this isn't true so,
x €empty

when, x < 0
x + x > 0
x > 0 this is also not possible so,
x€ empty

hence domain € empty

Answer 2

Answer:

Domain of this function is a Empty Set.

Step-by-step explanation:

Given function $f(x)=\frac{1}{\sqrt{x-|x|}}$

To find: Domain of function.

Domain of function is set of point for which function is defined.

So, we points where function is not defined then doman is set of real number excluding those points.

for x=0,

by putting x = 0 we get the denominator of f(x) = 0

⇒f(x) is not defined for x = 0

for x = positive real  no.

say x = a ∀ x∈$R^+$

$f(a)=\frac{1}{\sqrt{a-|a|}}\\\\=\frac{1}{\sqrt{a-a}} (Since, |x| \:gives \:positive\: value\: for\: all \:postive\: values)\\\\=\frac{1}{0}$

again denominator of f(x) gets equal to 0.

so, f(x) is not defined for x = positive real no.

for x = negative real no.

say x = a ∀ x∈$R^-$

$f(a)=\frac{1}{\sqrt{(-a)-|(-a)|}}\\\\=\frac{1}{\sqrt{-a-a}} (Since, |x| \:gives \:positive\: value\: for\: all \:negative\: values)\\\\=\frac{1}{\sqrt{-2a}}$

since Sqare root of negative value does not exit then the function f(x) is not defined for negative real no.

Therefore Domain of this function is a Empty Set.