Show that the distance measure defined as the angle between two data vectors, x and y, satisfies the metric axioms given on page 70. Specifically, angle between two data vectors is arccos( cos(x, y) ), so d(x, y) = arccos( cos(x, y) )Show for distance measure arccos( cos(x, y) )A) Positivity1) d(x, x) >= 0 for all x and y,2) d(x, y) == 0 onlY if x == y. B) Symmetryd(x, y) == d(y, x) for all x and y. C) Triangle Inequalityd(x, z) < d(x, y) + d(y, z) for all points x, y, and z. D) Explain in simple English the intuition for why would arccos( cos(x, y) ) satisfy the same properties (A, B,C above) as the Euclidean distance.

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation:

step-by-step explanation:

where is the question is there is a formula or is there not one