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
