1/(x-1)(x-3),find out the domain and range

Question

owlfred · Answer

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anonymous · Answer

the domain is all the real numbers except x=1 and x=3 as you cannot divide by 0. 
the range is all the real numbers, as the function is unbounded. (for example near x=1 it takes big values)

anonymous · Answer

(x-1)(x-3)
$$=x^2-4x+3$$
Its range is (-D/4a,infinity) $$(-1,\infty)$$

$$-1\le (x-1)(x-3) \le \infty$$
$$\infty > \frac{1}{(x-1)(x-3)} \ge 0$$
$$-1 \ge \frac{1}{(x-1)(x-3)} >-\infty$$

Therefore the range is,
$$R - (-1,0)$$

anonymous · Answer

Hey amogh... Is that a standard formula for finding range? (-D/4a,Infinity)

anonymous · Answer

For a quadratic equation, it is the minimum/maximum value (-b/2a,-D/4a) where D is the discriminant!