if f(x) = √x+2 and g(x) = √4-xsquare, then find the domain of f+g,fg , f/g.
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Hope u like my process
=====================
Given :-
=======
=> f(x) = (x+2)^½ and g(x) = (4-x²)^½
___________________
So,
For f+g
=-=-=-=-
When is square roots the terms can't be imaginary i.e. D≠ (-) ve for (D) ^½
So
First term will have D as negative when x < -2
So, x > - 2 according to 1st term.
Now,
In 2nd term,
D = negative when x>2 and x< - 2
So, it means x lies between - 2<x<2
So the required domain for f +g = (-2, 0)U(0,2)
____________________________
For fg
=-=-=-=-=
F(x). G(x) = (x+2)× [(2-x)^½]
For the term (2 - x) should not be negative!
So,
to get the values.
Thus the domain for fg lies at
(- infinity, 0)U(0,2)
____________________________
For f/g,
=-=-=-=-=
Now, the denominator should not be zero and
D≠ NEGATIVE, in (D) ^½
So,
X≠ 2
and,
So the domain of f/g lies at (-infinite, 0)U(0,1)
__________________________
Hope this is ur required answer
Proud to help you
=====================
Given :-
=======
=> f(x) = (x+2)^½ and g(x) = (4-x²)^½
___________________
So,
For f+g
=-=-=-=-
When is square roots the terms can't be imaginary i.e. D≠ (-) ve for (D) ^½
So
First term will have D as negative when x < -2
So, x > - 2 according to 1st term.
Now,
In 2nd term,
D = negative when x>2 and x< - 2
So, it means x lies between - 2<x<2
So the required domain for f +g = (-2, 0)U(0,2)
____________________________
For fg
=-=-=-=-=
F(x). G(x) = (x+2)× [(2-x)^½]
For the term (2 - x) should not be negative!
So,
to get the values.
Thus the domain for fg lies at
(- infinity, 0)U(0,2)
____________________________
For f/g,
=-=-=-=-=
Now, the denominator should not be zero and
D≠ NEGATIVE, in (D) ^½
So,
X≠ 2
and,
So the domain of f/g lies at (-infinite, 0)U(0,1)
__________________________
Hope this is ur required answer
Proud to help you
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