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
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