Answer to Question #45759 in Other Engineering for sapna

Question #45759
a) Which of the following functions are 1-1 and which are onto? Justify your answer. i) f : R ! R 0 given by f (x) = x 2 where R 0 is the set fx 2 Rjx 0g. ii) f : R ! R given by f (x) = x 2 + x + 1. (3) b) If we consider the expression 1 2 3x as a function on R, what will be its domain and range? Will it have an inverse? Justify your answer. (2) c) Let a = ( 1 2 p 2 ; p 3 2 p 2 ; 1 p 2 ) and b = ( 1 p 2 ; 0; 1 p 2 ) . i) Find the direct cosines of a and b. ii) Find the angle between a and b. (2) d) Check that the vectors u = ( 3 5 ; 4 5 ; 0 ) , v = ( 4 5 ; 3 5 ; 0 ) and w = (0; 0; 1) are orthonormal. Further, write the vector a = (1; 1; 2) as a linear combination of the vectors.
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