What is the domain and range of the function f given by f(x) = 2 - | x - 5 | ?

Asked by ahuja8087 | 10th Sep, 2015, 01:13: PM

Expert Answer:

D o m a i n space i s space t h e space s e t space o f space a l l space v a l u e s space t h a t space x space c a n space t a k e. S i n c e space minus infinity less than x less than infinity comma space d o m a i n space i s space t h e space s e t space o f space r e a l space n u m b e r s. D o m a i n colon x element of open parentheses negative infinity comma infinity close parentheses  R a n g e space i s space t h e space s e t space o f space a l l space v a l u e s space t h a t space y space c a n space t a k e.  W h e n space x rightwards arrow negative infinity comma space f open parentheses x close parentheses equals 2 minus open vertical bar x minus 5 close vertical bar rightwards arrow  stack l i m with x rightwards arrow negative infinity below open square brackets 2 minus open vertical bar x minus 5 close vertical bar close square brackets equals 2 minus stack l i m with x rightwards arrow negative infinity below open vertical bar x minus 5 close vertical bar space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 minus infinity space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals negative infinity  W h e n space x rightwards arrow infinity comma space space f open parentheses x close parentheses equals 2 minus open vertical bar x minus 5 close vertical bar rightwards arrow  stack l i m with x rightwards arrow infinity below open square brackets 2 minus open vertical bar x minus 5 close vertical bar close square brackets equals 2 minus stack l i m with x rightwards arrow infinity below open vertical bar x minus 5 close vertical bar space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 2 minus infinity space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals negative infinity T h e space f u n c t i o n space f open parentheses x close parentheses equals 2 minus open vertical bar x minus 5 close vertical bar space h a s space a space m a x i m u m comma space w h e n space open vertical bar x minus 5 close vertical bar equals 0. T h u s comma space t h e space f u n c t i o n space i s space h a v i n g space m a x i m u m space v a l u e space w h e n space x equals 5 comma space a n d space w h e n space x equals 5 comma space f open parentheses x close parentheses equals 2. T h u s comma space R a n g e space o f space f left parenthesis x right parenthesis colon space f open parentheses x close parentheses element of left parenthesis negative infinity comma 2 right square bracket

Answered by Vimala Ramamurthy | 10th Sep, 2015, 04:49: PM