5. If x, ye{0, 1, 2, 3, 4, 5} Then, which of the following are function in the given set?
(a) f1 = {(x, y): y = x - 1}
(b) f2 = {(x, y) : x + y < 3}
(c) fs = {(x, y): x > y}
(d) fa = {(x, y) : x + y = 4}

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) = .

Find the domain and range of the following function f(x) = 51x - 21+ 4

Which number line correctly shows 0.8 + 0.3?