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

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

Vedclass · Accepted Answer

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

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(A) The set $A$ contains all values of $x$ such that $f(x) = 0$.The set $B$ contains all values of $x$ such that $g(x) = 0$.The intersection $A \cap B$ contains all values of $x$ such that both $f(x) = 0$ and $g(x) = 0$ are satisfied simultaneously.For any real numbers $a$ and $b$,$a^2 + b^2 = 0$ if and only if $a = 0$ and $b = 0$.Therefore,$[f(x)]^2 + [g(x)]^2 = 0$ is equivalent to $f(x) = 0$ and $g(x) = 0$.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 $A \cap B$ is

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