ERROR ANALYSIS Describe and correct the error in the statement about the relation shown in the table. Input, x $1$ $2$ $3$ $4$ $5$
Output, y $6\frac{1}{2}$
$7\frac{1}{2}$
$8\frac{1}{2}$
$6\frac{1}{2}$
$9\frac{1}{2}$
X

The relation is not a function. One output is paired with two inputs.

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) = .