Question

if h(x)=3x,g(x)=x+2,f(x)=x²-1,are real functions such that hog of exists ,then (ho(gof))(2)=

Answer 1

 solution

given that h(x)=3x , g(x)=x+2 , f(x)=x²-1

let find (gof)(x)=(x²-1)+2 =x²+1

⇒ (gof)(x)=x²+1

then f(gof)(x)=3(x²+1)

    ⇒=3x²+3

f(gof)(2)=3(2²+3)

            =3(4+3)

           =3(7)

           =21