UI Composition of Functions Inverses of Each Other Exercise

Given the following functions, evaluate each of the following:
f(x) = x2 – 2x – 8
g(2) = x – 4
(f +9)(-3) =
(f-9)( – 4) =
(fºg)(4) =
=
(9)
( – 5) =
=
Function Operations
Given the functions:
f(x) = 5x
g(x) = 2x + 9
h(x) = 12×2 + 46%
36
Determine each of the following.
Give your answers as simplified expressions written in descending order.
g(x) + h(x) =
Find and simplify g(x) + h(2)
h(x) – g(x)
=
Find and simplify h(c) – 9(2)
f(x) h(x)
=
Find and simplify f(x).h(2)
h(2)
g(x)
=
1
h(2)
Find and simplify
hint: you will need to
g(2)
factor h(x)
g(x)
The domain restriction for is
f(a)
x +
Given that f(x) = 8x + 7 and g(2) = 7 – x2, calculate
(a) f(g(0)) =
(b) g(f(0)) =
Use the graphs to evaluate the expressions below.
6+
f(x)
5
8(x)
5
4
4
3
3
2
N
1
1
х
х
-1
1
2
3
4
5
6-1
1
2
3
4
5
& F-1
f(g(2))
g(f(4) =
=
f(f(0)
=
g(g(3))
=
Let f() = 5x + 5 and g(x) = 2×2 + 3x.
After simplifying,
(fog)(x) =
Question oln.
Video
Let f(x) =
1
X – 2
–
4
+ 2.
and g(2)
=
Find the following functions. Simplify your answers.
f(g(x)) =
g(f(x)) =
Move the slider k so that the graph of y = x2 gets shifted up 3 units. Then type the new function,
f(x) in the answer box
6
5
4
3
2
1
-4
-3
-2
-1
1
2
3
4
-1
f(x) = x2
k= 0.00
-2
o
+
Don’t forget to shift the graph up.
Using function notation, i.e. f(x) = , enter the function that results from the transformation.
Move the slider h so that the graph of y = x2 gets shifted to the right 3 units. Then type the new
function, f(a) in the answer box
4
3
2
1
-4
-3
-2
– 1
0
1
2
3
4
f(x) = x2
-1
O
h = 0.00
-2
– O ++ 1个
1 1 →
Don’t forget to shift the graph to the right.
Using function notation, i.e. f(x)=, enter the function that results from the transformation.
Move the sliders h and k so that the graph of y x2 gets shifted up 2 units and to the right 1 units.
Then type the new function, f(x) in the answer box
4
3
2
1
-4
-3
-2
-1
0
1
2
3
4
f(x) =
2
= 2
x2
-1
h = 0.00
-2
k= 0.00
– 0 ++ →
Don’t forget to shift the graph.
Using function notation, i.e. f(x) = , enter the function that results from the transformation.
5
3
2
1
-5 -4 -3 -2 -1
-1
1 2 3 4 5
-2
-3
-4
-5+
Write an expression for the function graphed above:
Enter abs(x) for (x).
6
5
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
1 2 3 4 5 6
-2
-5
-6
The graph above is a transformation of the function x2.
Give the function in the graph above.
g(x) =
Assume that the function f is a one-to-one function.
(a) If f(2) = 9, find f-1(9).
Your answer is
(b) If f-‘(- 6) = -5, find f(-5).
Your answer is
Let f(x) = (x – 2)2
Find a domain on which f is one-to-one and non-decreasing.
Find the inverse of f restricted to this domain.
f-1(x) =
Let f(x) = x + 2 and g(x) = x
– 2.
With the following stephs, determine whether f(x) and g(x) are inverses of each other:
(a) f(g(x)) =
(b) g(f(x)) =
(c) Are f(x) and g(2) inverses of each other?