a fx2x1 gxxx1 Find fg fgfg and fg with their DomainsSolution

a) f(x)=2/x+1, g(x)=x/x+1 Find: f+g, f-g,f*g and f/g with their Domains

Solution

a) f(x)=2/x+1, g(x)=x/x+1 Find:

f+g, Add the two function

(f +g)(x) = 2/(x+1) +x/(x+1) = (2+x)/(x+1)

Domain : all real except x =-1 ; ( -inf , -1)U (-1, inf)

f-g,( f -g)(x) Subtract the two functions

= 2/(x+1) - x/(x+1) = (2-x)/(x+1)

Domain : all real except x =-1 ; ( -inf , -1)U (-1, inf)

f*g : (f*g)(x) Just multiply the two functions and simplify

=[2/(x+1)]*x/(x+1) = 2x/(x+1)^2

Domain : all real except x =-1 ; ( -inf , -1)U (-1, inf)

f/g : f(x)/g(x) Just divide the two functions and simplify

= 2/(x+1) / x/(x+1) = 2/x

Domain : all real except x = 0 ; ( -inf , 0)U (0, inf)