This question is 87 points. this is a lot of points. use it wisely. respect the point.

Part a: select all of the ordered pairs that are located on the graph of the equation. part b: does the graph of the equation represent a function? select all correct answers for part a and one answer for part b.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Another type of subtraction equation is 16-b=7. explain how you would sole this equation then solve it.