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

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


   

Question 1179408: if 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!

if g%28x%29+=+3x%2B4, determine n such that g%28-3%29=g%5E-1%28n%29
g%28x%29+=+3x%2B4
then
g%28-3%29=3%2A%28-3%29%2B4
g%28-3%29=-5

now find g%5E-1%28x%29
g%28x%29+=+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

since g%28-3%29=g%5E-1%28n%29=-5 and g%5E-1%28x%29=x%2F3-4%2F3, replace x with n, then we have

g%5E-1%28n%29=n%2F3-4%2F3
-5=n%2F3-4%2F3
-15=n-4
-15%2B4=n
n=-11

check:

g%5E-1%28-11%29=-11%2F3-4%2F3=-5

Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.


            It can be solved in several lines,  as I will show it to you now. 


First,  g(-3) = 3*(-3) + 4 = -9 + 4 = -5.


So, they want you find "n" from the equation

    g%5E%28-1%29%28n%29 = -5.


This equation means that

    n = g(-5) = 3*(-5) + 4 = -15 + 4 = -11.


ANSWER.  n = -11.

Solved.

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The lesson to learn from my post is THIS:

            Think before writing a long many-lines solution:

            If you will think good and if you know the subject,  it may happen that the solution is in couple of lines.