SOLUTION: Consider the function f(x)= In(x-3). Find the inverse of f and call this function g(x). Evaluate g(5)..... I do not understand this problem or why we are switching from f to g.. He

Algebra ->  Functions -> SOLUTION: Consider the function f(x)= In(x-3). Find the inverse of f and call this function g(x). Evaluate g(5)..... I do not understand this problem or why we are switching from f to g.. He      Log On


   

Question 760115: Consider the function f(x)= In(x-3). Find the inverse of f and call this function g(x). Evaluate g(5)..... I do not understand this problem or why we are switching from f to g.. Help me please!!!!
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
The switching to the inverse function is because we want to be able to reverse a process. Just as we want to know how to open a door and walk through it, we also want to open the door and come back the other way. Just as we want to insert our foot into a shoe and tie the lace, we later want to untie the shoe and pull our foot out of it.

You have a logarithmic function f(x), and you put in some value for x and obtain some value of f(x) according to the defined formula. Later, you might want to use the function that if you give the function f(x), this other function would give you back x.

You are trying to find g(x) so that f%28g%28x%29%29=x and that f%28x%29=ln%28x-3%29.
You can start this way:
g(x)=?
You want g(x) to be the inverse of f%28x%29=ln%28x-3%29. You must have g%28f%28x%29%29=f%28g%28x%29%29=x.

f%28g%28x%29%29=ln%28%28g%28x%29%29-3%29=x
That says, the natural log of some expression is equal to x.
Converting into exponential form,
e%5E%28x%29=g%28x%29-3
g%28x%29-3=e%5Ex
highlight%28g%28x%29=3%2Be%5Ex%29