I f space t h e space f u n c t i o n space f colon A rightwards arrow B space d e f i n e d space b y space f open parentheses x close parentheses equals negative x squared plus 6 x minus 8 space i s space a space b i j e c t i o n comma space t h e n
d e f i n e space t h e space s e t s space A space a n d space B.

Please provide solution to this question

Asked by Topperlearning User | 25th Oct, 2016, 08:58: AM

Expert Answer:

begin mathsize 12px style Consider space the space given space function colon
straight f open parentheses straight x close parentheses equals negative straight x squared plus 6 straight x minus 8
rightwards double arrow straight y equals negative straight x squared plus 6 straight x minus 8
rightwards double arrow straight y equals negative straight x squared plus 6 straight x plus 9 minus 9 minus 8
rightwards double arrow straight y equals negative straight x squared plus 6 straight x minus 9 plus 9 minus 8
rightwards double arrow straight y equals negative open parentheses straight x squared minus 6 straight x plus 9 close parentheses plus 1
rightwards double arrow straight y minus 1 equals negative open parentheses straight x squared minus 6 straight x plus 3 squared close parentheses
rightwards double arrow negative open parentheses straight y minus 1 close parentheses equals open parentheses straight x minus 3 close parentheses squared
rightwards double arrow open parentheses straight x minus 3 close parentheses squared equals negative open parentheses straight y minus 1 close parentheses
From space the space above space equation comma space we space have comma
open parentheses 3 comma 1 close parentheses space is space the space vertxex space of space the space parabola.
And space 2 comma 4 space are space the space zeroes space of space the space quadratic space polynomial comma space minus straight x squared plus 6 straight x minus 8
Graphing space the space above space details space in space straight a space graph space paper comma space we space have
end style

T h e space p a r a b o l a space i s space s y m m e t r i c space a b o u t space t h e space l i n e space x equals 3
T h u s comma space w e space c a n space t a k e space v a l u e s space f o r space x space f r o m space minus infinity space t o space 3 space o r space f r o m space 3 space t o space infinity
I n space e i t h e r space c a s e comma space t h e space v a l u e s space o f space y space w i l l space b e space minus infinity space t o space 1.
T h u s comma space A equals left parenthesis negative infinity comma 3 right square bracket space a n d space B equals left parenthesis negative infinity comma 1 right square bracket

Answered by  | 25th Oct, 2016, 10:58: AM