Question

f(x)=x²-4x+5 and g(x)=6-x² what is (g o f)(x) and
(f(x+h)-f(x)) / (h)

Answer 1

(g o f)(x) = g(f(x))
g(x) = 6 - x^2
replace x in g(x) with x^2 - 4x + 5

Answer 2

(6-x)²-4(6-x)+5

Answer 3

What you have done is f(g(x)). That is, you substituted g(x) in the place of x in f(x).
But they want g(f(x)). Since g(x) = 6 - x^2, g(f(x)) = 6 - ( f(x) )^2
g(f(x)) = 6 - (x^2 - 4x + 5)^2

Answer 4

okay and then you just factor that out but what is really bugging me is the second half of the question

Answer 5

For the above, I don't know if they expect you to expand the square and simplify or just leave it as it is. Check your answer choices to see which one works.
For the second part:
f(x) = x^2 - 4x + 5
f(x+h) means replacing x by (x+h)
f(x+h) = (x+h)^2 - 4(x+h) + 5
f(x+h) - f(x) = (x+h)^2 - 4(x+h) + 5 - x^2 + 4x - 5 =
x^2 + 2xh + h^2 - 4x - 4h + 5 - x^2 + 4x - 5 =
2xh + h^2 - 4h

{ f(x+h) - f(x) } / h = (2xh + h^2 - 4h) / h = 2x + h - 4