Functions f and g are given as follows Fx 5x 2 gx xx 2 F

Functions f and g are given as follows. F(x) = 5/x + 2 g(x) = x/x + 2 Find each of the following functions and state its domain. f + g f - g f + g f/g g/f (f + g)(x) = Simplify your answer.)

Solution

a)f+g

=(⁵/_x+2)+(^x/_x+2)

=(^5+x/_x+2)

domain is (-,-2)U(-2,)

b)f-g

=(⁵/_x+2)-(^x/_x+2)

=(^5-x/_x+2)

domain is (-,-2)U(-2,)

c)f*g

=(⁵/_x+2)*(^x/_x+2)

=(^5x/_x+2)

domain is (-,-2)U(-2,)

d)f/g

=(⁵/_x+2)/(^x/_x+2)

=(⁵/_x)

domain is (-,-2)U(-2,0)U(0,)

e)g/f

=(^x/_x+2)/(⁵/_x+2)

=(^x/₅)

domain is (-,-2)U(-2,)