How would I go about answering these questions on Characteristics of Functions?

Question

1. Given f(x)=3x+2 and g(x)=-2x+1
2. write an equation for (f+g)(x)
3. Determine (f+g)(6)
4. determine (fg)(x)
5. determine (f-g)(x)
6. determine domain of (f÷g)(x)
7. Given g(x)=cosx and g(x)=sinx
8. determine (fog)(pi)
9. determine (g^-1og)(x)

Answer 1

Given f(x) = 3x + 3 and g(x) = -2x + 1

(f+g)(x) would equal the sum of f and g

(3x+3) + (-2x+1) = x + 4

(f+g)(6) would equal the sum of f and g while plugging in 6 for x

(3x+3) + (-2x+1) = x + 4 = (6) + 4 = 10

(fg)(x) would equal f times g using FOIL

(3x+3) (-2x+1) = -6x² + 3x - 6x + 3 = -6x² - 3x + 3

(f-g)(x) would equal the difference of f and g

(3x+3) - (-2x+1) = (3x+3) + (2x-1) = 5x + 2

Given g(x)=cosx and g(x)=sinx



(fog)(pi) would equal g inside of f with pi plugged in as x

cos(sin(pi)) = cos(0) = 1

(g^-1og)(x) would equal g inside the inverse of g

sin^-1(sin(x)) = x