SOLUTION: g(x) = 3x+4, determine n such that g(-3) = g^-1(n):

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Question 1180065: g(x) = 3x+4, determine n such that g(-3) = g^-1(n):
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


determine such that
first find
......replace with
.....swap variables
........solve for


=> => it will be

now find



then find


...both sides multiply by




Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

Solve it in two steps, each step is in one line.


    Step 1.   g(-3) = 3*(-3) + 4 = -9 + 4 = -5.


    Step 2.   Now you need to find n from equation  -5 = .    (*)

              Apply function g to both sides of (*).  Do not calculate the function  explicitly:  YOU DO NOT NEED do it.

              Simply remember that  = .    (**)

              After applying function g to both sides of (*), you have g(-5) = n,  or  n = g(-5) = 3*(-5)  + 4 = -15 + 4 = -11.    ANSWER

Solved.

---------------

MEMORIZE:  this problem is not to calculate the function    explicitly.

                    This problem is to check,  if you do understand  WHAT  the inverse function    is,  in general;
                    in particular,  if you do understand equality  (**).



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