Find (g o f)(x), given:

f(x) = x+1 and g(x) = x2 - x.

(g o f)(x)  is the same as g(f(x))

f(x) = x+1              g(x) = x² - x

g(f(x)) =  g(x+1)

Note g(x) = x² - x, therefore g(x+1) would be that anywhere we see x in g(x) we replace it with (x+1)

g(x) = x² - x

g(x+1) = (x+1)² - (x+1)  =  x² + 2x +1 - x - 1 =  x² + 2x-x +1 -1 =   x² + x 

Therefore  (g o f)(x) =  x² + x 

Absolute value graph shifted point 5 up