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Question Number 10741 by okhema last updated on 24/Feb/17

a f u n c t i o n f i s d e f i n e d b y f (x) = \frac{x + 3}{x - 1}, x n o t e q u a l t o 1 . d e t e r m i n e w h e t h e r f i s b i j e c t i v e, t h a t i s, b o t h o n e t o o n e a n d o n t o

Answered by mrW1 last updated on 24/Feb/17

f (x) = \frac{x + 3}{x - 1} = y

x + 3 = y x - y

x (y - 1) = 3 + y

x = \frac{y + 3}{y - 1}

\Rightarrow f (x) i s b i j e c t i v e .

Commented by okhema last updated on 24/Feb/17

y e s t h a t s t h e w o r k i n g o u t b u t f r o m y o u r a n s w e r

h o w c o u l d y o u t e l l t h a t s i t s b i j e c t i v e

Commented by mrW1 last updated on 24/Feb/17

f o r e a c h x w e g e t a n u n i q u e y .

i t s h o w s f o r e a c h y w e g e t a l s o a n

u n i q u e x .

t h u s t h e f u n c t i o n i s b i j e c t i v e .

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