if g(x)= 1/x+1 then the inverse function g⁻¹(x)=

Answer 1

g(x) : y = 1/ (x+1)

To find g^-1(x), just swap y and x, then solve for y again:

x = 1/(y+1)

y+1 = 1/x

y = 1/x - 1

Make sure to double check your arithmetic, knowing that composite functions of inverses always = x.

Check (g ¤ g^-1)(x)= 1/((1/x)-1) + 1) = 1/(1/x) = x

Check Again (g^-1 ¤ g)(x) = 1/(1/(x+1))-1 = x+1-1 = x