05-07_task
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Virgil I. Grissom High School *
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Course
MATH
Subject
Mathematics
Date
Nov 24, 2024
Type
Pages
2
Uploaded by ElderNeutron3900
Name:
Jesus Hernandez
Date:
11-8-2023
School:
Grissom High School
Facilitator:
Mrs. Walker
5.07 Inverse Functions (45 Points)
Complete the charts.
1.
Find the inverse of
f
(
x
) = 4
x
+ 1, showing every step. Then verify that it is an inverse.
Inverse of
f
(
x
) - Step
f
(
x
) = 4
x
+ 1
4 > 4x + 1
x > 44 + 1 (-1)
x - 1 = 44 (x4)
= 4
𝑥−1
4
(x) =
𝑓
−1
1−1
4
Verify that it is an inverse.
Find
f
(
f
-1
(
x
)). Show your work step by
step.
Find
f
-1
(
f
(
x
)) . Show your work step by
step.
f
(
f
-1
(
x
)) =
f
-1
(
f
(
x
)) =
(14
+1)-1)14 = 9
𝑥
2
4(x-1)14+1
x+2-1 = 4
(x-1)+1
x = 4
x+2-1 = 4
x = 4
x = 4
(x-1)+1
x = 4
2.
Find the inverse of
f
(
x
) = 2
x
²
−
3, showing every step. Then verify that it is an inverse.
Inverse of
f
(
x
) - Step
f
(
x
) = 2
x
2
– 3
4 = 2
-3
𝑥
2
x =
-3(-3)
24
2
x+3 =
(-3)
24
2
© ACCESS Virtual Learning 2021
=
(
)
𝑥+3
3
4
2
−
3
= 4
2
𝑥+2
2
2
Verify that it is an inverse.
Find
f
(
f
-1
(
x
)). Show your work step by
step.
Find
f
-1
(
f
(
x
)) . Show your work step by
step.
f
(
f
-1
(
x
)) =
f
-1
(
f
(
x
)) =
(
)+
= 4
(2𝑥2 − 3
5
2
2(
)x-3 = 4
2 + 2 − 1𝑥
1x = 4
(2𝑥 − 2 + 3)
(2x+6/x) = 4
x
3-3 = 4
·
x = 4
(x+2)-3 = 4
x =4
3.
Find the inverse of
f
(
x
) = (
x
+ 1)
2
+ 6, showing every step. Then verify that it is an
inverse.
Inverse of
f
(
x
) - Step
f
(
x
) = (
x
+ 1)
2
+ 6
(4+1
+6 = 4
)
2
+24+1+6 = 4
4
2
+24+7 = 4
4
2
x =
+24+7
4
2
x =
+24+7
4
2
Verify that it is an inverse.
Find
f
(
f
-1
(
x
)). Show your work step by
step.
Find
f
-1
(
f
(
x
)) . Show your work step by
step.
f
(
f
-1
(
x
)) =
f
-1
(
f
(
x
)) =
((2
)+1)2+6 = 7
𝑥 − 7
(2
)x-7x6 = 4
𝑥 + 1
(x-7)+1x6 = 4
x+1-7+6 = 4
x = 4
x = 4
© ACCESS Virtual Learning 2021
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