Answer:
y = (x-2)⁵+2
Step-by-step explanation:
y = 1 + [tex]\sqrt[5]{x-2}[/tex]
inverse is switching x and y
x = 1+ [tex]\sqrt[5]{y-2}[/tex]
x-1 = [tex]\sqrt[5]{y-2}[/tex]
(x-1)⁵= y-2
y = (x-1)⁵+2
The inverse is (x-1)^5 +2
y = 1 + (x-2) ^ 1/5
Exchange x and y
x = 1 + (y-2) ^ 1/5
Solve for y
Subtract 1 from each side
x-1 = 1-1 +(y-2) ^ 1/5
x-1 = (y-2) ^ 1/5
Raise each side to the 5th power
(x-1) ^5 = (y-2) ^ 1/5^5
(x-1)^5 = y-2
Add 2 to each side
(x-1)^5 +2= y-2+2
(x-1)^5 +2= y
