1. g(n)=4n-5 f(n)=n^2-3n Find (g-f)(n) 2. g(t)=4t+1 f(t)=4t Find (g times f)(t) 3. h(n)=n-5 g(n)= 2n+2 Find (h/g)(n) 4. f(x)=2x-2 find (f times f)(x) 5. g(t)=-3t+4 f(t)-3t^3+3t Find (g times f) (t)

Answer 1

g=4n-5

f = n^2-3n

g-f = 4n-5 -n^2+3n = 7n-n^2-5

g=4t+1

f = 4t

gf = (4t+1)(4t) = 16t^2 +4t

h=n-5

g=2n+2

h/g = (n-5)/(2n+2) = (n-5)/2(n+1)

which also = 1/2 -3/(n+1)

= 1/2 with remainder -6

f= 2n-2

f^2 = ff = (2n-2)^2 = 4(n-1)^2

= 4(n^2-2n+1)

=4n^2-8+4

g=-3t+4

f= -3t^3+3t

gf = (-3t+4)(-3t^3+3t)

= 3t^4 -12t^3 -9t^2 +12t

f= f(x), g=g(x), h=h(x)

to "simplify" and avoid repeating what f,g or h are functions of what variable, x every time