SOLUTION: If {{{ g(x) = 3 + x + e^x }}} , find {{{ g^-1(4) }}} Me and my friend are so stuck on this problem. We have no clue how to solve it. We switched the x values and y values but go

Question 217256: If , find
Me and my friend are so stuck on this problem. We have no clue how to solve it. We switched the x values and y values but got stuck on:

Could you please help us out! Thanks in advance. =)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
You've done everything correctly so far. Now we're looking for . If we replace x by 4 in your equation for the inverse we get:

which simplifies to

which leaves us with figuring out y. Other than some logic, combined with trial and error, the only way to find y that I can suggest is to look at the graph of g(x). (I'd suggest looking at the graph of the inverse but Algebra.com's graphing software will not work on .)

Since the function's x's are the inverse's y's and vice versa and since we are looking for , we can try to find where g(x) = 4. And from the graph it appears that g(0) = 4. And we can verify this by substituting 0 in for x and finding g(0) (which does indeed turn out to be 4). Since g(0) = 4 then .
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