## anonymous 5 years ago 1/(x-1)(x-3),find out the domain and range

1. Owlfred

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2. anonymous

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)

3. anonymous

(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, $R - (-1,0)$

4. anonymous

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

5. anonymous

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