9 For the function Fn r 1 use composition of functions to sh

9. For the function, F(n) r+ 1, use composition of functions to show that fiI is as given: )

Solution

f(x) =(2/5) x+1

f^-1(x)=(5x-5)/2

(fof^-1)(x) = f((5x-5)/2) =(2/5)(5x-5)/2 +1 =x-1+1=x

(f^-1of)(x)=f^-1((2/5)x+1) =(5((2/5)x +1)-5)/2=2x/2=x

since (fof^-1)(x)=(f^-1of)(x)=x

Therefore the inverse is f^-1(x)=(5x-5)/2