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

Algebra ->  Test -> 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      Log On


   

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(20855) About Me  (Show Source):
You can put this solution on YOUR website!

i)
let a positive number be x,
then add four to the number and you get
x%2B4
Next, square the resulting number,
%28x%2B4%29%5E2
and multiply result by 3,
3%28x%2B4%29%5E2
Finally, divide the result by 2,
%283%28x%2B4%29%5E2%29%2F2
If you’re his friend and you get a result of 50,
%283%28x%2B4%29%5E2%29%2F2=50

ii)
now solve for x
%283%28x%2B4%29%5E2%29%2F2=50
3%28x%2B4%29%5E2=50%2A2
%28x%2B4%29%5E2=100
3%28x%5E2+%2B+8x+%2B+16%29=100
3x%5E2+%2B+24x+%2B+48-100=0
3x%5E2+%2B+24x+-52=0
need positive solution
x+=+10%2Fsqrt%283%29+-+4
the exact original number is +10%2Fsqrt%283%29+-+4
or approximate
x+=1.7735026918962582




Answer by ikleyn(53937) About Me  (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 %282y%29%2F3;

       - take the square root from it, getting  sqrt%28%282y%29%2F3%29;

       - subtract 4 from it, getting  sqrt%28%282y%29%2F3%29-4.


     It is your inverse function  x = sqrt%28%282y%29%2F3%29-4.    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 = sqrt%28%282%2A50%29%2F3%29-4 = sqrt%28100%2F3%29-4 = 10%2Fsqrt%283%29-4 = 1.773502692...    ANSWER

Solved.