Solution Instead of applying the values of x directly in the given function, we may simplify the function and apply the values of x one by one given in the table lim x>2 (x 2)/ (x2 x 2) Since we have a quadratic function in the denominator, we may find factors and simplify = lim x>2 (x 2)/ (x 2) (x 1)You also asked if f(x) 2 and f(x 2) are different Yes they are The placement of the parentheses makes a difference For example with your graph above, when x = 4, f(x) = 0 and hence f(x) 2 =0 2 = 2 But f(x 2) = f(4 2) = f(2) = 2 In the second expression, since 4 2 is inside the parentheses you evaluate it first to get 2The values of the function ( y values ) in the table of values for f(x) = x 2 1 are all one higher than the corresponding values in the table of values for g(x) = x 2 and the graph has been translated vertically by 1 unit Note that the grah of f(x) = x 2 1 does not cross the x axis This tells us that the equation x 2 1 = 0 has no solution We know this already as a squared number is
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