Find the inverse of f (x) = 1 + square root (1+x)

Here is the best answer in the world x^2-2x

To find inverse

replace f (x) with y

replace all x with y and all y with x

solve for y

replace y with f⁻¹ (x)

so

f (x) = 1+√ (1+x)

y=1+√ (1+x)

x=1+√ (1+y)

minus 1 both sides

x-1=√ (1+y)

square both sides

x²-2x+1=1+y

minus 1 both sides

x²-2x=y

f⁻¹ (x) = x²-2x

the inverse is f⁻¹ (x) = x²-2x