# If #f(7+x)=f(7-x), forall x in RR# and #f(x)# has exactly three roots #a,b,c#, what is the value of #a+b+c#?

The given condition implies that the function is symmetric about the point ( x = 7 ). Since ( f(x) ) has exactly three roots, and the function is symmetric about ( x = 7 ), the roots must occur in pairs on either side of ( x = 7 ). Let's denote these roots as ( a ) and ( b ) on one side of ( x = 7 ), and ( c ) on the other side.

Thus, the sum of the roots ( a + b + c ) equals ( 7 + 7 = 14 ). Therefore, ( a + b + c = 14 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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