SOLUTION: Let f(x)=x+2 and g(x)=x/3. Also denote the inverses to these functions as f^{-1} and g^{-1}. Compute f(g^{-1}(f^{-1}(f^{-1}(g(f(19)))))).

Algebra ->  Functions -> SOLUTION: Let f(x)=x+2 and g(x)=x/3. Also denote the inverses to these functions as f^{-1} and g^{-1}. Compute f(g^{-1}(f^{-1}(f^{-1}(g(f(19)))))).      Log On


   



Question 1091007: Let f(x)=x+2 and g(x)=x/3. Also denote the inverses to these functions as f^{-1} and g^{-1}. Compute f(g^{-1}(f^{-1}(f^{-1}(g(f(19)))))).
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

There is nothing complicated about this except the notation. You just need to make sure you start with the innermost parentheses -- which means you work from right to left to evaluate the given expression.

As for the notation, let me use F and G for the inverses of the two given functions.

And of course you need to know that

f%28x%29=x%2B2 --> F%28x%29=x-2
and
g%28x%29=x%2F3 --> G%28x%29=3x

Then...
f%2819%29=21
g%2821%29=7
F%287%29=5
F%285%29=3
G%283%29=9
f%289%29=11