SOLUTION: If {{{ g(x) = 3 + x + e^x }}}, find {{{ g^-1(4) }}} Me and my friend are working on this problem together. We started by switching the x values with the y values: {{{ x = 3 +

Algebra ->  Inverses -> SOLUTION: If {{{ g(x) = 3 + x + e^x }}}, find {{{ g^-1(4) }}} Me and my friend are working on this problem together. We started by switching the x values with the y values: {{{ x = 3 +      Log On


   

Question 217239: If +g%28x%29+=+3+%2B+x+%2B+e%5Ex+, find +g%5E-1%284%29+
Me and my friend are working on this problem together. We started by switching the x values with the y values:
+x+=+3+%2B+y+%2B+e%5Ey+
Then we subtracted 3 from each side:
+x-3+=+y+%2B+e%5Ey+
We tried taking the ln of each side but got really confused. Can you please help us with this problem. Thanks in advance. =)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You cannot explicitly solve for 'y' since you have a 'y' term buried in an exponent and another part of a binomial. In other words, you can't solve equations of the form x%2Bb%5Ex=0 for 'x' exactly.


What you can do is realize what they're really asking. They're not asking for an inverse function (although it would be nice to know it). They just want the 'x' value that results in a 'y' value of 4.


Remember that the inverse function simply maps values from the range back to the domain. The function g(x) sends a value 'x' to 'y'. The inverse function just brings 'y' back to 'x'.


So all you need to find is the value of 'x' that makes g%28x%29=4. You can either guess and check, use a table, or a calculator.


In either method, you'll find that g%280%29=4. This means that (just apply the inverse to both sides of the last equation).


Let me know if you have questions about the answer.