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Answer:
Third option
x ≠2 and x cannot be any value for which v(x) = 0
Step-by-step explanation:
In this problem we are asked to find the domain of the function
We know that .
We know that:
Domain of U(x) is all real numbers except <em>x = 0</em>
Domain of V(x) is all real numbers except <em>x = 2</em>.
Then the domain of the composite function U(V (x)) is:
all real numbers except <em>x = 2</em>. (since <em>x = 2</em> does not belong to the domain of V(x) and all values of x for which <em>V(x) = 0</em> (since <em>x = 0</em> does not belong to the domain of U(x))
Finally the domain of ) is:
and