Question

The inverse equation

Answer 1

The inverse is (x-1)^5 +2

Explanation:

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

The inverse is (x-1)^5 +2

Answer 2

y = (x-2)⁵+2

Explanation:

y = 1 +
`\sqrt[5]{x-2}`

inverse is switching x and y

x = 1+
`\sqrt[5]{y-2}`

x-1 =
`\sqrt[5]{y-2}`

(x-1)⁵= y-2

y = (x-1)⁵+2