Determine-whether-f-x-1-x-2x-2-1-is-1-A-function-2-injective-3-surjective-4-bijective-

Question Number 192286 by pete last updated on 14/May/23

Determine whether f (x) = \frac{1}{x} ({2 x}^{2} + 1) is :

1 . A function

2 . injective

3 . surjective

4 . bijective

Answered by mehdee42 last updated on 14/May/23

i f y = 1 \Rightarrow 2 x^{2} - x + 1 = 0 \Rightarrow x = \frac{1 \pm \sqrt{- 3}}{4} \notin R \Rightarrow f i s n o t s u r j e c t i v e

f (a) = f (b) \Rightarrow (a - b) (2 a b - 1) = 0 \Rightarrow a = b \lor a = \frac{1}{2 b} \Rightarrow f i s n o t i n j e c t i v e

Commented by mehdee42 last updated on 14/May/23

Commented by pete last updated on 14/May/23

thank you sir

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