
Functions
Presentation
•
Mathematics
•
10th Grade
•
Medium
Maman Firmansyah
Used 19+ times
FREE Resource
12 Slides • 20 Questions
1
Functions
Inverse and composite functions
2
Learning Objectives
Understand about inverse of a function
Determine of inverse of a functions
Form composite functions
3
Multiple Choice
Which of the following relation represents a function?
{(1,2), (1,3), (2,3)}
{(1,2), (1,3), (1,4)}
{(1,2), (2,3), (2,3)}
{(1,2), (2,3), (3,3)}
4
Multiple Choice
Is this graph a function or not a function?
Function
Not a Function
5
Multiple Choice
6
Multiple Choice
R: {0, 1, 2, -4}
R:{1, -3, -4}
R:{1, -3, -4}
7
Review
If input is 4, output is 3, OR f(4) = 3
If output is 3, input is 4 OR f-1(3) = 4
.
What is f(1), f-1(1)?
What is f-1(x)?
8
9
10
11
Multiple Choice
12
Multiple Choice
Given: f(x)=2x−3 .
What is f−1(1)?
−1
1
2
8
13
Multiple Choice
Determine f-1(2) given the following information about an invertible function, f(x)
f(1) = -3
f(2) = -2
f(-1) = 2
f(3) = -1
1
-1
2
-2
14
Do all functions have inverse?
If a function gives the same value of y for two or more values of x, it does not have an inverse function.
15
Functions with inverse
If a horizontal line cuts the graph of a function at most once, then that function has an inverse.
16
Functions with NO inverse
If a horizontal line cuts the graph more than once, then that function does not have an inverse.
17
Multiple Choice
Which graph passes the horizontal line test?
Graph 1
Graph 2
Graph 3
Graph 4
18
Multiple Choice
Does this graph have an inverse?
Yes
No
19
Multiple Choice
Does this graph have an inverse?
Yes
No
20
21
22
23
Multiple Choice
g(x) = x - 2
Find f(g(5))
24
Multiple Choice
f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))
16
4
-4
None of these.
25
Multiple Choice
If f(x) = 3x-1 and g(x) = x2+2,
what is (f ° g)(x) ?
3x2 +5
x2 +1
3x2 +1
3x2 +6
26
Multiple Choice
If f(x)=x2 and g(x)=x21 find (f∘g)(−1)
41
1
−1
−41
27
Multiple Choice
If f(x)=x1 and g(x)=3x+2 find (g∘g)(−4)
44
-40
-30
-28
28
Multiple Choice
If f(x)=x1 and g(x)=3x+2 find (f∘g)(2)
41
81
27
8
29
Multiple Choice
If f(x)=2x and g(x)=2x2−1 find g(f(x))
4x2−1
4x2−2
8x2−1
16x2−1
30
Multiple Choice
If f(x)=2x and g(x)=2x2−1 find f(g(x))
4x2−1
4x2−2
8x2−1
16x2−1
31
Multiple Choice
If f(x)=2x and g(x)=2x2−1 find g(f(−1))
2
15
7
-9
32
Multiple Choice
If f(x)=2x and g(x)=2x2−1 find f(g(3))
34
71
35
142
Functions
Inverse and composite functions
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