Given the functions fx 3x x2 and gx x squareroot x find

Given the functions f(x) = 3x - x^2 and g(x) = x + squareroot x, find the following and simplify: No need to find any domains. Simplify completely. a. (f - g) (x) B).(g/F) (x) c) (F compositefunction g) (x)

Solution

f(x) = 3x - x^2

g(x) = x+ sqrt x

a) ( f- g)(x) = f(x) - g(x)

= 3x - x^2 - x - sqrt x

= -x^2 + 2x - sqrt x

b) (g/f)(x) = g(x) / f(x)

(x+ sqrt x) / ( 3x - x^2 )

c) ( fo g)(x)

= 3 ( x+sqrt x) - ( x+ sqrt x)^2

3x + 3 sqrt x - ( x^2 + x + 2 x sqrt x)

3x + 3 sqrt x - x^2 - x - 2 x sqrt x

-x^2 + 2x + ( 3 - 2x) sqrt x