that in differential equations we determine the functions that satisfy the differential equations. Some times the functions are linearly dependent and some times they are linearly independent. In each of the following questions, please determine whether the given functions are linearly independent or dependent for the given intervals. Justify your answer.

(1) f (x) = Absolute (x) and f (x) = x on ( 0 , 10 )

(2) f (x) = Absolute (x) and f (x) = x on ( -10 , 0 )

Question

that in differential equations we determine the functions that satisfy the differential equations. Some times the functions are linearly dependent and some times they are linearly independent. In each of the following questions, please determine whether the given functions are linearly independent or dependent for the given intervals. Justify your answer.

(1)  f (x) = Absolute (x)   and     f (x) = x     on    ( 0 , 10 )    

(2)  f (x) = Absolute (x)   and     f (x) = x     on    ( -10 , 0 )