Question

Which function is the inverse of f(x) = (x - 1)^2, if f(x) is restricted to the domain $1 \leqslant \times \ \textless \ \infty$

Answer 1

f(x) = (x-1)²

left y = f(x)

y = (x - 1)²

solve for x

Take the square root of both-side

√y = x - 1

Add 2 to both-side of the equation

√y + 1 = x

Substitute y by x and x by f⁻'(x)

√x + 1 = f⁻'(x)

f⁻'(x)= √x + 1