y-x-2-x-Find-the-set-of-values-of-the-function-

Question Number 180391 by Shrinava last updated on 11/Nov/22

y = x - \frac{2}{x}

Find the set of values of the function .

Commented by Shrinava last updated on 11/Nov/22

Answer : (- \infty; + \infty)

Answered by aleks041103 last updated on 12/Nov/22

x \in R \Rightarrow \forall y \in I, \exists x \in R, y = x - \frac{2}{x}

\Rightarrow x^{2} - y x - 2 = 0

f o r t h i s t o h a v e a s o l n i n t h e R :

D = y^{2} - 4 (1) (- 2) = y^{2} + 8 > 0 \Leftrightarrow y \in R

\Rightarrow a n s . I = (- \infty, + \infty) \equiv R

Commented by Shrinava last updated on 12/Nov/22

thank you dear professor