The function f(x) and g(x) are shown on the graph. F(x)= |x|
What is g(x)?

Enter the missing numbers in the boxes to complete the table of equivalent ratios of lengths to widths. ? 18 8 ? 10 30 12 ?

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) = .

Explain how you can show five less than a number using algebraic expression