SOLUTION: Vilakazi and his friend are playing a number guessing game. Vilakazi asks his friend to think a positive number, then add four to the number. Next, square the resulting number, a

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Question 1195961: Vilakazi and his friend are playing a number guessing game. Vilakazi asks his friend to think
a positive number, then add four to the number. Next, square the resulting number, and
multiply result by 3. Finally, divide the result by 2. If you’re his friend and you get a result of
50,
i)
Write an inverse function that will give you an original number; and [ 5 marks]
ii)
Determine the original number. [ 5 marks
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

i)
let a positive number be ,
then add four to the number and you get

Next, square the resulting number,

and multiply result by ,

Finally, divide the result by ,

If you’re his friend and you get a result of ,


ii)
now solve for






need positive solution

the exact original number is
or approximate





Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

(i)  In order for to write the inverse function, let's denote the resulting number by "y"


     After that, write the arithmetic and algebraic operations in reverse order,
     starting from y.


       - Multiply "y" by 2, getting 2y;

       - divide 2y by 3, getting ;

       - take the square root from it, getting  ;

       - subtract 4 from it, getting  .


     It is your inverse function  x = .    ANSWER

     It allows you calculate the starting number x from the resulting number y.



(ii)  To determine the starting number, use this function with the value y = 50.

      You will get  x =  =  =  = 1.773502692...    ANSWER

Solved.



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