If A = {x : f(x) = 0} and B = {x : g(x) = 0}, | vedclass

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(A) The intersection of two sets $A$ and $B$,denoted by $A \cap B$,is the set of all elements that are common to both $A$ and $B$.By definition,$A \ca

Vedclass · Accepted Answer

${[f(x)]^2} + {[g(x)]^2} = 0$

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(A) The intersection of two sets $A$ and $B$,denoted by $A \cap B$,is the set of all elements that are common to both $A$ and $B$.By definition,$A \cap B = \{x : x \in A 	ext{ and } x \in B\}$.Given $A = \{x : f(x) = 0\}$ and $B = \{x : g(x) = 0\}$,the intersection is $A \cap B = \{x : f(x) = 0 	ext{ and } g(x) = 0\}$.For real-valued functions,the condition $f(x) = 0$ and $g(x) = 0$ is equivalent to the condition ${[f(x)]^2} + {[g(x)]^2} = 0$,because the sum of squares of two real numbers is zero if and only if each number is zero individually.

If $A = \{x : f(x) = 0\}$ and $B = \{x : g(x) = 0\}$,then $A \cap B$ will be

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