Find-the-range-of-f-x-x-5-x-2-4-

Question Number 27847 by NECx last updated on 15/Jan/18

F i n d t h e r a n g e o f f (x) = \frac{x + 5}{x^{2} - 4}

Commented by NECx last updated on 16/Jan/18

p l e a s e h e l p

Answered by prakash jain last updated on 17/Jan/18

y = \frac{x + 5}{x^{2} - 4}

x^{2} y - x - (4 y + 5) = 0

x \in R \Rightarrow Δ ⩾ 0

{(- 1)}^{2} - 4 (y) (-) (4 y + 5) ⩾ 0

1 + 16 y^{2} + 20 y ⩾ 0

16 y^{2} + 20 y + 1 ⩾ 0

(y - (- \frac{5}{8} + \frac{\sqrt{21}}{8})) (y - (- \frac{5}{8} - \frac{\sqrt{21}}{8})) ⩾ 0

∵ A quadratic expression has sine

same as coefficient of x^{2} except in

between roots .

y \in (- \infty, - \frac{5}{8} - \frac{\sqrt{21}}{8}] \cup [- \frac{5}{8} + \frac{\sqrt{21}}{8}, \infty)

Commented by Rasheed.Sindhi last updated on 16/Jan/18

Pl insert some more steps between

last two steps .