Question

Part 1.] Determine the equation of the inverse of
`y= (1)/(4) x^(3) -2`

A.]
`y= \sqrt[3]{4x+2}`
B.]
`y= \sqrt[3]{4x-2}`
C.]
`y= \sqrt[3]{4x+8}`
D.]
`y= \sqrt[3]{4x-8}`
E.]
`y= \sqrt[3]{ (1)/(4)x-2}`

Part 2.] Determine the equation of the inverse of
`y=e^(x+3) -4`.
A.]
`y=ln(x+4)-3`
B.]
`y=ln x+1`
C.]
`y= (1)/(3)( (x)/(e)+4)`
D.]
`y= (1)/(4)lnx-3`

Answer 1

y = 1/4 x^3 + 2
1/4 x^3 = y - 2
x^3 = 4(y - 2)

x = cube root (4y - 8)

inverse y = cube root (4x - 8)

Its D.