#1.)
Given and ; find a function such that .
I'm having trouble determining what should be - I don't know the method to determine this. If I was just asked to find any two functions whos composition resulted in ) I would have just decomposed as and - but I'm obviously forced to use the inside function .
#2.)
Given find . In other words, solve for in .
I posted #2 in a previous thread, but I didn't really get the response I was looking for - I would appreciate the explanation for the answer if possible.
Your g(x) does not result in 4x-4 when composed with f(x) = x+3 as the inner function. However, thank you for pointing me in the right direction, since it appears g(x) = 4x-16 works.
But I still would like to know the steps to approach problems like these, since the method of trial and error in finding a correct function seems impractical later on.
And the 2nd question is still giving me problems...I simply don't know what to do with the logarithm when the variable I am solving for is in two separate terms...
Thanks bud, appreciate the explanation.
Any suggestions on the 2nd problem? I started by isolating the natural logarithm, them setting each term as an exponent with base 'e' (thus isolating 1 'y' by itself). But then the other 'y' becomes an exponent which can only be isolated by going back to the original equation and taking the natural logarithm of both sides...Whatever I try, I end up with ugly terms -