2 votes 2 votes Let $f(x)$ mean that function $f$ ,applied to $x$,and $f^{n}(x)$ mean $f(f(........f(x)))$,that is $f$ applied to $x$ ,$n$ times.Let $g(x) = x+1$ and $h_{n}(x)=g^{n}(x).$Then what is $h_{9}^{8}(72)?$ Set Theory & Algebra discrete-mathematics set-theory&algebra functions + – Lakshman Bhaiya asked Oct 7, 2018 Lakshman Bhaiya 576 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply MiNiPanda commented Oct 7, 2018 reply Follow Share 144? 0 votes 0 votes daksirp commented Oct 7, 2018 reply Follow Share @minipanda, $h_{9}$ is fine, but what is $h_{9}^{8}$ 0 votes 0 votes Lakshman Bhaiya commented Oct 7, 2018 reply Follow Share @MiNiPanda Yes 144 is the right answer can you explain? 0 votes 0 votes MiNiPanda commented Oct 7, 2018 reply Follow Share First compute h9(x) Given: hn(x)=gn(x) , g(x)= x+1 g2(x)= g(g(x)) = g(x+1)=(x+1)+1 =x + 2*1 g3(x)= g(g(g(x))) = g(g2(x))=g(x+2)= (x+2)+1 = x+3 = x+ 3*1 Seeing this pattern we can infer that g9(x) = x+ 9*1=x +9 So, h9(x)=g9(x)=x+9 Now we have to compute h98(x) where x=72 h91(x) = x+9 h92(x) = h9(h9(x)) = h9(x+9) = (x+9) +9 = x+2*9 h93(x) = h9(h9(h9(x))) = h9(h92(x))= h9(x+2*9) = (x+2*9) +9 = x+3*9 Again following the same pattern we can conclude that h98(x) = x +8*9 =x+72 Put x=72 , it becomes 72+72=144 6 votes 6 votes manohar commented Oct 7, 2018 reply Follow Share Why dont you put that as an answer. 0 votes 0 votes Lakshman Bhaiya commented Oct 8, 2018 reply Follow Share @MiNiPanda This is the nice method I think this you add to the answer 0 votes 0 votes Please log in or register to add a comment.