Function arithmetic

f(x)= x    g(x)= x+1
(f+g)(x) = (f+g)(2)= f(2)+g(2)=
(f-g)(x) = (f-g)(2)= f(2)-g(2)=
(g-f)(x) = (g-f)(2)= g(2)-f(2)=
(fg)(x) = (fg)(2)= f(2)g(2)=
(f/g)(x) = (f/g)(2)= f(2)/g(2)=
(g/f)(x) = (g/f)(2)= g(2)/f(2)=

f(x)= x    g(x)= x2
(f+g)(x) =
(f-g)(x) =
(g-f)(x) =
(fg)(x) =
(f/g)(x) =
(g/f)(x) =

f(x)= 2x-3    g(x)= -4x+5
(f+g)(x) =
(f-g)(x) =
(g-f)(x) =
(fg)(x) =
(f/g)(x) =
(g/f)(x) =

f(-x) flips over Y-axis.
-f(x) flips over X-axis.
-f(-x) flips over both X-axis and Y-axis; equivalent to 180° rotation about origin.

If f(x)=f(-x), then f is Even (symmetric across the Y-axis). Also: -f(x)=-f(-x)
If f(-x)=-f(x), then f is Odd (symmetric about the Origin). Also: f(x)=-f(-x)

f(x)= -3x2 + 5
f(-x) =
-f(x) =
-f(-x) =
f(3x) =
f(-3x) =
f(x+1) =

f(x)= -3x
f(-x) =
-f(x) =
-f(-x) =
f(3x) =
f(-3x) =
f(x+1) =

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

f(x)= x3 + 2x2 - 3x + 5
f(-x) =
-f(x) =
-f(-x) =
f(3x) =