Find-domain-amp-range-of-function-f-x-1-x-2-5x-6-

Question Number 96383 by bobhans last updated on 01/Jun/20

Find domain & range of function

f (x) = \frac{1}{x^{2} - 5 x + 6}

Answered by john santu last updated on 01/Jun/20

The domain consists of all real

number except 2 and 3 . To determine

the range, set y = \frac{1}{x^{2} - 5 x + 6}

and solve for x . \Rightarrow x^{2} - 5 x + (6 - \frac{1}{y}) = 0

This has solution when and only

when b^{2} - 4 a c = 25 - 24 + \frac{4}{y} ⩾ 0

This holds if only if \frac{4}{y} ⩾ - 1

this holds when y > 0, and if

y < 0, when y ⩽ - 4 . Hence the

range is (- \infty, - 4] \cup (0, \infty)

Commented by bemath last updated on 01/Jun/20

thank you for the explanation