Math, asked by tanya45090, 1 year ago

if f(x) = √x+2 and g(x) = √4-xsquare, then find the domain of f+g,fg , f/g.

Answers

Answered by rakeshmohata
8
Hope u like my process
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Given :-
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=> f(x) = (x+2)^½ and g(x) = (4-x²)^½
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So,
For f+g
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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)
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For fg
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F(x). G(x) = (x+2)× [(2-x)^½]

For the term (2 - x) should not be negative!

So,
x \leqslant 2
to get the values.

Thus the domain for fg lies at
(- infinity, 0)U(0,2)
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For f/g,
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 \frac{f(x)}{g(x)}  =  \frac{1}{ \sqrt{2 - x} }
Now, the denominator should not be zero and

D≠ NEGATIVE, in (D) ^½

So,

X≠ 2

and,
x &lt; 2
So the domain of f/g lies at (-infinite, 0)U(0,1)
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Hope this is ur required answer

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