inverse function
TRANSCRIPT
![Page 1: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/1.jpg)
Inverse Functions
![Page 2: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/2.jpg)
Not all functions have inverse functions. A function has an inverse function
if and only ifthe function is a one to one relation.
![Page 3: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/3.jpg)
Determine whether each of the following functions has an inverse function. Given reasons for your answers.
Yes, the function has an inverse function.
![Page 4: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/4.jpg)
Determine whether each of the following functions has an inverse function. Given reasons for your answers.
N0, the function does not has an inverse function (not an one –to-one relation)
2
3
4
5
![Page 5: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/5.jpg)
Determine whether each of the following functions has an inverse function. Given reasons for your answers.
Yes, the function has an inverse function.
0
2
4
6
A
0
1
2
3
B
![Page 6: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/6.jpg)
Determine whether each of the following functions has an inverse function. Given reasons for your answers.
0
1
2
3
4
A
0
2
4
6
B
N0, the function does not has an inverse function (not an one –to-one relation)
![Page 7: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/7.jpg)
)3(1f )(1 xf
The function f is defined as f(x) = 2x – 5. Find (a) (b)
3 2x - 5
2x 3+5
x
8
2
84
4)3(1 f
x 2x - 5
2x x+5
x 2
5x
2
5)(1
x
xf
![Page 8: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/8.jpg)
)3(1f )(1 xf
The function f is defined as f(x) = 2x – 5. Find (a) (b)
yf )3(1let 3)( yf
352 y532 y
82 y28y
4y4)3(1 f
yxf )(1let xyf )(
xy 5252 xy
2
5
xy
2
5)(1
x
xf
![Page 9: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/9.jpg)
xxf 49)( (a)
,
Find the inverse function fˉ¹(x) for each of the function f(x) below.
y 9 – 4x- 4x y - 9
x 4
9
y
4
9)(1
xxf
4
9
y
4
9
y
4
9 y
![Page 10: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/10.jpg)
xxf
10)( (b)
,
Find the inverse function fˉ¹(x) for each of the function f(x) below.
xxf
10)(1
yx
10
10
xy
1
xy
10
0, x
![Page 11: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/11.jpg)
3
2)(
x
xxf(c)
,
Find the inverse function fˉ¹(x) for each of the function f(x) below.
x
xxf
1
23)(1
3
2
x
x
2x)3( xy yxy 3
1, x
x23 yxy
23 y xyx )1( yx
y
y
y
1
23 x23 y
![Page 12: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/12.jpg)
43)( xxf(d)
,
Find the inverse function fˉ¹(x) for each of the function f(x) below.
3
4)(1
x
xf
43 x
x34y
y
3
4y x
![Page 13: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/13.jpg)
14
1)( xxf(e)
,
Find the inverse function fˉ¹(x) for each of the function f(x) below.
)1(4)(1 xxf
14
1x
x4
11y
y
)1(4 y x
![Page 14: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/14.jpg)
2
3)(
xxf(f)
,
Find the inverse function fˉ¹(x) for each of the function f(x) below.
23
)(1
xxf
2
3
x
3
2xy
1
y
y
3 2x
23
y
x
0, x
![Page 15: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/15.jpg)
4
32)(
x
xxf(g)
,
Find the inverse function fˉ¹(x) for each of the function f(x) below.
x
xxf
2
34)(1
4
32
x
x
32 xyxy 4
y
34 y xyx 2
34 y )2( yx
2, x
3xy
y
y
2
34 x
![Page 16: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/16.jpg)
)(1 xf (a)
2. Given that f(x) = x – 5 and g(x) =
5)(1 xxf
1
2
x
x
x5y
y
Find
and )3(1f
5x
(a)
53)3(1 f
8
![Page 17: Inverse Function](https://reader033.vdocument.in/reader033/viewer/2022061116/5465bfa8b4af9ff3478b491c/html5/thumbnails/17.jpg)
)(1 xg (b)
2. Given that f(x) = x – 5 and g(x) =
x
xxg
1
2)(1
1
2
x
x
2xyxy
y
2 yxy x2 y xyx
1, x
y
y
1
2 x
Find
and )2(1g
1
2
x
x
2 y )1( yx
(b) x
xxg
1
2)(1
21
22)2(1
f
1
4
4