Question

find a formula for the inverse g(x)=(x-6)^3

Answer 1

first change g(x) into y
\[\implies y = (x-6)^3\]
now interchange x and y
\[\implies x = (y - 6)^3\]
solve for y
\[\implies \sqrt[3] x = y -6\]
add 6 to both sides
\[\implies \sqrt[3] x + 6 = y\]
does that help?