1 Give an example of a function fx with a domain of 05 and a

1. Give an example of a function, f(x), with a domain of (0,5] and a range of [O,oo)
2. If f(t) = 2t-t2, what is (f(t+h)- f(t) )/h?
3. If F= {1,2), (3,5), (4,7)} and G ={(1,4), (3,0), and (5,2)}, what is F+G? What is F\\G(using function arithmetic)?

Solution

1. Give an example of a function, f(x), with a domain of (0,5] and a range of [O,oo)

Domain start from 5 exchuding 5:

Examle : f(x) =ln(x-5)

WFor log functions domain should be such that (x-5)>0

x>5

2) If f(t) = 2t-t2, what is (f(t+h)- f(t) )/h

f(t+h) = 2(t+h) - (t+h)^2 = 2(t+h)[ 1 - t -h] = 2t +2h - t^2 -h^2 -2th

(f(t+h)- f(t) )/h =( 2t +2h - t^2 -h^2 -2th  - 2t - t^2)/h

= ( 2h - 2t^2 -h^2 -2th)/h

= 2 - 2t^2/h - h -2t