document.write( "Question 1118646: Find f(7)+f^-1(7) if f(3x-2)=x+5 \n" ); document.write( "

Algebra.Com's Answer #734019 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "I don't know a formal way for finding f(x) from the given information. Perhaps another tutor will also respond with a different method than I use.

\n" ); document.write( "For me, f(3x-2) = x+5 means that f(x) is of the form $\"f%28x%29+=+%28x%2F3%29%2Bb\"$ .

\n" ); document.write( "To find b, use the given fact that f(3x-2) = x+5:

\n" ); document.write( " $\"f%283x-2%29+=+%283x-2%29%2F3+%2B+b+=+x%2B5\"$
\n" ); document.write( " $\"x-2%2F3%2Bb+=+x%2B5\"$
\n" ); document.write( " $\"b+=+5%2B2%2F3+=+17%2F3\"$

\n" ); document.write( "So

\n" ); document.write( " $\"f%28x%29+=+%28x%2F3%29%2B17%2F3\"$

\n" ); document.write( "Then

\n" ); document.write( " $\"f%287%29+=+7%2F3+%2B+17%2F3+=+24%2F3+=+8\"$

\n" ); document.write( "To find f^-1(7), set f(x)=7 and solve for x:

\n" ); document.write( " $\"7+=+%28x%2F3%29%2B17%2F3\"$
\n" ); document.write( " $\"4%2F3+=+x%2F3\"$
\n" ); document.write( " $\"x+=+4\"$

\n" ); document.write( "Finally, then, f(7)+f^-1(7) = 8+4 = 12. \n" ); document.write( "

\n" );