Question

Part 1.] Determine the equation of the inverse of $y= \frac{1}{4} x^{3} -2$
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.] $y= \sqrt[3]{ \frac{1}{4}x-2}$

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.] $y= \frac{1}{3}( \frac{x}{e}+4)$
D.] $y= \frac{1}{4}lnx-3$

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.