f(x)=sqareroot of(sin[x]+cos[x]) find domain and range 

Asked by Kalyanrao Chavan | 26th Aug, 2014, 08:48: AM

Expert Answer:

G i v e n f open parentheses x close parentheses equals square root of open parentheses sin space x space plus space cos space x close parentheses end root  A b o v e space f u n c t i o n space c a n space b e space w r i t t e n space a s f open parentheses x close parentheses equals square root of fraction numerator square root of 2 over denominator square root of 2 end fraction cross times open parentheses sin space x space plus space cos space x close parentheses end root equals square root of square root of 2 cross times open parentheses fraction numerator 1 over denominator square root of 2 end fraction sin space x space plus space fraction numerator 1 over denominator square root of 2 end fraction cos space x close parentheses end root equals open parentheses 2 close parentheses to the power of 1 fourth end exponent cross times square root of open parentheses sin space open parentheses straight pi over 4 plus x close parentheses close parentheses end root  A b o v e space f u n c t i o n space i s space d e f i n e d space w h e n space open parentheses sin space open parentheses straight pi over 4 plus x close parentheses close parentheses space i s space n o n space n e g a t i v e. space rightwards double arrow straight pi over 4 plus x space m u s t space l i e space i n space 1 s t space a n d space s e c o n d space q u a d r a n t. space 2 n straight pi less or equal than straight pi over 4 plus straight x less or equal than open parentheses 2 straight n plus 1 close parentheses straight pi straight x element of open square brackets 2 straight n straight pi minus straight pi over 4 comma space open parentheses 2 straight n plus 1 close parentheses straight pi minus straight pi over 4 close square brackets space is space the space domaon space of space given space function  We space know space that space range space of space sin space straight x space is space open square brackets minus 1 comma space 1 close square brackets comma space Here space non space negative space values space are space only space allowed. space So space space range space of space straight f left parenthesis straight x right parenthesis space is space open square brackets 0 comma space 2 to the power of 1 fourth end exponent close square brackets

Answered by Dharma Teja | 26th Aug, 2014, 02:32: PM