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

Algebra ->  Functions -> SOLUTION: g(x) = 3x+4, determine n such that g(-3) = g^-1(n):      Log On


   

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

g%28x%29+=+3x%2B4
determine n such that g%28-3%29+=+g%5E-1%28n%29
first find g%5E-1%28x%29
g%28x%29+=+3x%2B4......replace g%28x%29+ with y
y=+3x%2B4.....swap variables
x=+3y%2B4........solve for y
x-4=+3y
y=x%2F3-4%2F3
=> g%5E-1%28x%29=x%2F3-4%2F3=> it will be g%5E-1%28x%29=+g%5E-1%28n%29

now find g%28-3%29+
g%28-3%29+=+3%28-3%29%2B4
g%28-3%29+=+-9%2B4
g%28-3%29+=+-5
then find
g%5E-1%28n%29=-5
-5=n%2F3-4%2F3
-5%2B4%2F3=n%2F3...both sides multiply by 3
-15%2B4=n
n=-11


Answer by ikleyn(52796) About Me  (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 = g%5E%28-1%29%28n%29.    (*)

              Apply function g to both sides of (*).  Do not calculate the function g%5E%28-1%29%28x%29 explicitly:  YOU DO NOT NEED do it.

              Simply remember that g%28g%5E%28-1%29%28n%29%29 = n.    (**)

              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.

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MEMORIZE:  this problem is not to calculate the function  g%5E%28-1%29  explicitly.

                    This problem is to check,  if you do understand  WHAT  the inverse function  g%5E%28-1%29  is,  in general;
                    in particular,  if you do understand equality  (**).