If the function f:[2,∞)→[1,∞)  is defined by f(x)=3x(x−2) , then f−1(x)  is

Let g(x)  be the inverse of f , then f(g(x))=x . ⇒   3g(x)(g(x)−2)=x⇒   (g(x))2−2g(x)−log3x=0 ⇒   g(x)=2±4+4log3x2=1±1+log3x Since g:[1,∞)→[2,∞).  so g(x)=1+1+log3x .