inverse function
TRANSCRIPT
Inverse Functions
Not all functions have inverse functions. A function has an inverse function
if and only ifthe function is a one to one relation.
Determine whether each of the following functions has an inverse function. Given reasons for your answers.
Yes, the function has an inverse function.
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
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
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)
)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
)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
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
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
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
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
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
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
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
)(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
)(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