Given the function hn 4 3nn 6 evaluate the following expr

Given the function h(n) = 4 - 3/n/n + 6, evaluate the following expressions. h(1) = h(2) - h(-2) = h(2t) = h(s + 1) = Use interval notation to represent the domain of this function.

Solution

h(n) = (4 - 3/n) / (n + 6)

h(2t) = ( 4 - 3/(2t) ) / (2t + 6)

==> h(2t) = [(8t - 3)/(2t)] / (2t + 6)

==> h(2t) = (8t - 3)/[2t(2t + 6)]

h(s + 1) ==> replace 2t by s + 1

==> h(s + 1) = (4(s + 1) - 3)/[(s + 1)(s + 1 + 6)]        

==> h(s + 1) = (4s + 4 - 3)/[(s + 1)(s + 7)]      

==> h(s + 1) = (4s + 1)/[(s + 1)(s + 7)]

for the function to be defined the denominators should not be zero

==> n 0 and n + 6 0

==> n 0 and n -6

Hence domain is (- , -6) U (-6 , 0) U (0 , )