Feg 1034 Calculus & Analysis 1
Autor: Sharon • November 14, 2018 • 665 Words (3 Pages) • 465 Views
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Hence, = is horizontal asymptotes for .
FEG 1034 Calculus & Analysis 1 7
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FEG 1034 Calculus 1 Chapter 02[pic 35]
[pic 36]
2.2 Inverse Functions
[pic 37]
= 2 + 1
[pic 38][pic 39]
is input, is output, but what if I want as output, as input? You need to reverse the function, how to do?
Let = 2 + 1
= −21, this time your is output, as input, we can express in
−1= −2 1
[pic 40][pic 41][pic 42][pic 43]
−1 = 2
−1
+ 1 = and −1
=
2 +1 −1
=
2
2
[pic 44][pic 45]
FEG 1034 Calculus & Analysis 1 8
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FEG 1034 Calculus 1 Chapter 02[pic 46]
[pic 47]
−1 = −1 =
[pic 48][pic 49][pic 50]
What is the characteristic of inverse functions?
- It will always reflect its’ function on = line
- Since it reflect on = line,
−1 = ⟹ =
[pic 51][pic 52][pic 53]
- need one to one function, then have the existence of −1 !
[pic 54]
How to determine one to one function?
FEG 1034 Calculus & Analysis 1
9
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FEG 1034 Calculus 1 Chapter 02[pic 55]
[pic 56]
Horizontal line test
If the graph have any intersect horizontal line twice or more, then it’s not one to one function.
[pic 57]
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FEG 1034 Calculus 1 Chapter 02[pic 58]
[pic 59]
First derivative test
[pic 60]
If the function can be derived and if function doesn’t have inverse function.
[pic 61]
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′ = 0, then the
[pic 62]
= 3 + − 1
= 3 − + 1
′ = 3 2 + 1 = 0
′ = 3 2 − 1 = 0
3 2 + 1 = 0
3 2 − 1 = 0
2 = −
1
= ±
1
3
3
Since 2 can’t be negative in
′
= 0 when = ±
1
3
Real number, so ′ ≠ 0
does not have −1
Hence, −1 exist.
[pic 63][pic 64][pic 65][pic 66][pic 67][pic 68][pic 69]
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FEG 1034 Calculus 1 Chapter 02[pic 70]
[pic 71]
2.3 Derivative of inverse function
[pic 72]
is a function,
′ is tangent slope ofat , point.
−1 is its’ inverse function,
−1 ′ is tangent slope of −1 at , point.
[pic 73][pic 74][pic 75][pic 76][pic 77][pic 78][pic 79]
−1 ′ =
1
Reciprocal value
′
[pic 80][pic 81]
FEG 1034 Calculus & Analysis 1 12
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FEG 1034 Calculus 1 Chapter 02[pic 82]
[pic 83]
2.3 Derivative of inverse function
= 2 ′ = 2
−1 is its’ inverse function,
−1 ′ is tangent
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