Question

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

Answer 1

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

Answer 2

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