If f:[0, ) [2, ) is given by f(x)=x+ 1 x , then f⁻¹(x) equals

Step-by-step solution

Let f(x)=y=x+ 1 x or x y=x²+1 or x²-x y+1=0 Since, x [0, ) D 0 y²-4 0 y [2, ) x= y y²-4 2 x= y- y²-4 2 or x= y- y²-4 2 f⁻¹(y)= y+ y²-4 2 or f⁻¹(y)= y- y²-4 2 Replace by x , f⁻¹(x)= x+ x²-4 2 or f⁻¹(x)= x- x²-4 2