If f(x)= x^2 + 3 and g(x) = 3x - 1 then find the following:
1a. (f+g)(x)
1b. (f+g)(3)
1c. (f-g)(x)
1d. (fg)(x)
1e. (fg)(-1)
1f. (f/g)(x)
1g. (f o g)(x)
1h. (f o g)(1)
1i. (g o f)(x)
1a)
(f+g)(x) = f(x)+g(x) = (x^2+3) + (3x-1) = x^2 + 3x + 2
1d)
(fg)(x) = f(x) g(x) = (x^2+3)(3x-1) = 3x^3 - x^2 + 9x - 3
1f)
(fog)(x) = f(g(x)) = g^2+3 = (3x-1)^2 + 3 = 9x^2 - 6x + 4
1i)
(gof)(x) = g(f) = 3f-1 = 3(x^2+3)-1 = 3x^2 + 8
The others should be easy from here.