# If f(x) has a property that f(2-x) = f(2+x) for all x and f(x) has exactly 4 real zeros, how do you find their sum?

If ( f(x) ) has the property ( f(2-x) = f(2+x) ) for all ( x ), then it has symmetry about the line ( x = 2 ).

If ( f(x) ) has exactly 4 real zeros, then these zeros occur symmetrically around ( x = 2 ).

To find their sum, you add the zeros in pairs:

( (x_1 + x_2) + (x_3 + x_4) ), where ( x_1 ) and ( x_2 ) are zeros on one side of ( x = 2 ), and ( x_3 ) and ( x_4 ) are zeros on the other side.

If you know the values of the zeros, plug them into this equation to find their sum.

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8

The total of all four zeroes is eight, since each pair of zeroes adds up to four.

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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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