document.write( "Question 217256: If $\"+g%28x%29+=+3+%2B+x+%2B+e%5Ex+\"$ , find $\"+g%5E-1%284%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "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:\r
\n" ); document.write( "\n" ); document.write( " $\"+x-3+=+y+%2B+e%5Ey+\"$ \r
\n" ); document.write( "\n" ); document.write( "Could you please help us out! Thanks in advance. =) \n" ); document.write( "

Algebra.Com's Answer #163827 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
You've done everything correctly so far. Now we're looking for $\"g%5E-1%284%29\"$ . If we replace x by 4 in your equation for the inverse we get:
\n" ); document.write( " $\"4-3=y%2Be%5Ey\"$
\n" ); document.write( "which simplifies to
\n" ); document.write( " $\"1=y%2Be%5Ey\"$
\n" ); document.write( "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 $\"x-3=y%2Be%5Ey\"$ .)
\n" ); document.write( " $\"graph%28600%2C+600%2C+-8%2C+8%2C+-8%2C+8%2C+3%2Bx%2Be%5Ex%29\"$
\n" ); document.write( "Since the function's x's are the inverse's y's and vice versa and since we are looking for $\"g%5E%28-1%29%284%29\"$ , 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 $\"g%5E%28-1%29%284%29+=+0\"$ . \n" ); document.write( "

\n" );