range-of-function-y-x-1-x-3-

Question Number 85425 by john santu last updated on 22/Mar/20

r a n g e o f f u n c t i o n

y = \frac{∣ x - 1 ∣}{x + 3}

Answered by john santu last updated on 22/Mar/20

f o r x ⩾ 1 \Rightarrow y = \frac{x - 1}{x + 3}

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

w e g e t : 0 ⩽ y < 1

f o r x < 1 \Rightarrow y = \frac{- x + 1}{x + 3}

x = \frac{- 3 y + 1}{y + 1}, w e g e t y < - 1 \lor y ⩾ 0

t h e r e f o r e r a n g e i s y < - 1 \lor y ⩾ 0

Commented by jagoll last updated on 22/Mar/20

Commented by jagoll last updated on 22/Mar/20

this the graph

Answered by MJS last updated on 22/Mar/20

y = {\begin{cases} \frac{1 - x}{x + 3} = - 1 + \frac{4}{x + 3}; x < 1 \\ \frac{x - 1}{x + 3} = 1 - \frac{4}{x + 3}; x ⩾ 1 \end{cases}

range = {\begin{cases} R_{1} = R ∖ [- 1; 0] \\ R_{2} = [0; 1 [ \end{cases}

range : R = R_{1} \cup R_{2} = R ∖ [- 1; 0 [

or R =] - \infty; - 1 [\cup [0; + \infty [

Commented by john santu last updated on 22/Mar/20

m y a n s w e r c o r r e c t o r w r o n g ?

Commented by john santu last updated on 22/Mar/20

i {d o n}^{'} t u n d e r s t a n d t h e

n o t a t i o n] - \infty; - 1 [?

i t s a m e t o (- \infty, - 1) ? s i r

Commented by $@ty@m123 last updated on 22/Mar/20

Y e a h .

B o t h a r e s a m e .