2530.51 – Defined Operation 3; Do Composition

Here are two functions, hh and bb, along with some examples of what they do.

  • 3h=103h = 10

  • 7h=507h = 50

  • 5h=265h = 26

  • 4b=14b = 1

  • 7b=2.57b = 2.5

  • 20b=920b = 9

So OK then, what is nn if nhbnhb = 17.5?

(Notation: this means start with n, do h to it, and then do b to that.)

Solution

Let's look at the values we've been given and see if we can find a pattern:

h: 3 \rightarrow 10, 7 \rightarrow 50, 5 \rightarrow 26, so x \rightarrow x^2 + 1

b: 4 \rightarrow 1 ,7 \rightarrow 2.5 ,20 \rightarrow 9 , so x \rightarrow x/2 – 1

hb: n \rightarrow \rightarrow 17.5

n^2 + 1 \rightarrow 17.5 : we did h to n and now we do b

(n^2 + 1)/2 - 1= 17.5 : we did b to nh giving (n^2 + 1)/2 -1 = n^2/2 – 1/2 = 17.5

n^2 = 36

n = ±6