Question

Write the inverse of f(x)=1\9(x-4)^2

Answer 1

f(x) does not pass the horizontal line test, so its inverse is not a function.

Write it as y = f(x), then interchange variables and solve for y.
y = (1/9)(x - 4)²
x = (1/9)(y - 4)²
9x = (y - 4)²
±3√x = y - 4
y = 4 ± 3√x

f⁻¹(x) = 4 ± 3√x