[الراكز]

The graph of the function is given in blue. Use transformations to create the function whose graph is shown in red.
y = 6x − x2
y = 1
.................................................. .................................................. .................................................. ...........................
Find each of the following functions and state their domains.
f(x) = x3 + 4x2
g(x) = 7x2 - 2
(c) fg =
.................................................. .................................................. .................................................. .............................. Find each of the following functions and their domains.
f(x) = x2 - 1
g(x) = 4x - 1
(a) f g = 1

2x 1
(-, )
x > 4
(-, 1]


(b) g f = 3

4x 1
x > 4
(-, )
(-, 1]


(c) f f = 5

6x 1
x > 4
(-, )
(-, 1]


(d) g g = 7

.................................................. .................................................. ....................... Find f g h.
f(x) = √x − 5
g(x) = x2
h(x) = x3 + 9
1
.................................................. .................................................. ......................... (a) If g(x) = 2x + 1 and h(x) = 4x2 + 4x + 9, find a function f such that f g = h. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)
f = 1

(b) If f(x) = 2x + 4 and h(x) = 2x2 + 2x + 2, find a function g such that f g = h.
g(x) = 2