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

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Question

(A) The set $A$ contains all $x$ such that $f(x) = 0$.The set $B$ contains all $x$ such that $g(x) = 0$.The intersection $A \cap B$ contains all $x$ s

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The set $A$ contains all $x$ such that $f(x) = 0$.The set $B$ contains all $x$ such that $g(x) = 0$.The intersection $A \cap B$ contains all $x$ such that $f(x) = 0$ $AND$ $g(x) = 0$.If $f(x) = 0$ and $g(x) = 0$,then the sum of their squares must also be zero,i.e.,${[f(x)]^2} + {[g(x)]^2} = 0$.Thus,$A \cap B = \{x : {[f(x)]^2} + {[g(x)]^2} = 0\}$.

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

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