F (x) = 8x / x - 2 g (x) = 6/x+3 determine the domain of f + g

Given f (x) = 2x + 3 and g (x) = - x2 + 5, find (f o f) (x). (f o f) (x) = f (f (x))

= f (2x + 3)

= 2 () + 3 ... setting up to insert the input

= 2 (2x + 3) + 3

= 4x + 6 + 3

= 4x + 9 Given f (x) = 2x + 3 and g (x) = - x2 + 5, find (g o g) (x). (g o g) (x) = g (g (x))

= - () 2 + 5 ... setting up to insert the input

= - (-x2 + 5) 2 + 5

= - (x4 - 10x2 + 25) + 5

= - x4 + 10x2 - 25 + 5

= - x4 + 10x2 - 20

Sometimes you have to be careful with the domain and range of the composite function.

Given f (x) = sqrt (x) and g (x) = x - 2, find the domains of (f o g) (x) and (g o f) (x).