Recall that cosh : R H [1, 00), cosh(x) = (ex te x) Finding the inverse of this function is a delicate process because cosh is not one-to-one By restricting the domain of this function to make it monotonic, the restricted function will have an inverse. First we find intervals where the function is monotonic. The derivative of cosh () is BE , from which we deduce tha 1/2*(exp(x)+exp(-x))=0 . the only stationary point of cosh(x) is at x = 0 cosh(x) is monotonic decre.. for & 0 This gives us two choices for cosh () corresponding to intervals where cosh (a) is monotonic 1. the left branch cosh : (-0o, 0] #> [1, co] 2. the right branch cosh : [0, 0o) > [1, oo] . The functions y = cosh(r) and y = I are plotted below in red and blue. The two possible inverse functions for cosh(r) are plotted in green. Match the branches with their inverse functions. Function Graph (green) 3 7 O Inverse of left branch O Inverse of right branch W - O Inverse of left branch 4 O Inverse of right branch N/a * 1012 4