Explain why f(x) = x−4 is not the identical function of g(x) = x2 −7x + 12/ x−3 .

Question

Explain why f(x) = x−4 is not the identical function of g(x) = x²−7x +12/ x−3

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Answer 1

g(x) = (x² - 7x + 12) / (x - 3) = [(x - 4)(x - 3)] / (x - 3) = x - 4, when x ≠ 3

The graphs of y = f(x) and y = g(x) are identical for all x ≠ 3. At x = 3, y = g(x) is undefined. The graph of

y = g(x) is the same as the graph of y = f(x) except for a "hole" at the point (3, -1).