Define a function f on a set of real numbers as follows: f(x) = 3x − 1 x , for each real number x ≠ 0 Prove that f is one-to-one. Proof: Let x1 and x2 be any nonzero real numbers such that f(x1) = f(x2). Use the definition of f to rewrite the left-hand side of this equation. (Enter the answer as an expression in x1.) Then use the definition of f to rewrite the right-hand side of f(x1) = f(x2). (Enter the answer as an expression in x2.) Equate the expressions obtained for the left- and right-hand sides of f(x1) = f(x2), and simplify the result completely. The result is the following equation. x1 = Therefore, f is .

I've been working on this for a few days and i just don't understand, it's due in a few hours. you. the direction of a vector is defined as the angle of the vector in relation to a horizontal line. as a standard, this angle is measured counterclockwise from the positive x-axis. the direction or angle of v in the diagram is α.part a: how can you use trigonometric ratios to calculate the direction α of a general vector v = < x, y> similar to the diagram? part bsuppose that vector v lies in quadrant ii, quadrant iii, or quadrant iv. how can you use trigonometric ratios to calculate the direction (i. e., angle) of the vector in each of these quadrants with respect to the positive x-axis? the angle between the vector and the positive x-axis will be greater than 90 degrees in each case. part cnow try a numerical problem. what is the direction of the vector w = < -1, 6 > ?