Let a be an integer. Prove that 2a C 1 and 4a2 C 1 are relatively prime.

L5 - 10 Now You Try It (NYTI): 1. Graph the functions below using transformations of the exponential func- tion. Keep track of how the point (0,1) and the asymptote y =0ear transformed and include them in the graph. −x (a) f(x)=0(1 − e ) (b) f(x)=2 − e −(x+1) 2. Find the domain of each of the following functions of x: (a) f(x)= √ 1 − e ▯ x (b) f(x)= 1+ e x 3. The following are one-to-one functions. Find a formula for the inverse func- tion in each case; be mindful of the restrictions on the domainofthefunction and its inve▯se. ▯ x 2 (a) f(x)=n 2 , x> 0 √ 1+ x (b) f(x)= 2 − e 4. Find the domain for each function of x below: (a) f(x)=(1 − e ) ▯ ln(x) (b) f(x)= 2 − ex 5. A very small tumor of size M is observed every ten days, and over each ten-day period it grows 50% larger. (a) Write a formula representing the size of the tumor after t days (t = 0,10,20,... ) (b) At which value of t will we ﬁnally observe the tumor is more than 10 times its original size (c) How many times greater than its original size will the tumor be on day 100