document.write( "Question 978054: Find the domain and range of the function f(x) =x ^2 - 2x-3/x^2+2x+3 and hence find expression for f(3x+1) and determine f(4) \n" ); document.write( "

Algebra.Com's Answer #599548 by josgarithmetic(39618) $\"\"$ $\"About$

You can put this solution on YOUR website!

, and the denominator has no real roots and it positive everywhere. Zeros of f(x) are at x=-1 and x=3.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-infinity to -1,
\n" ); document.write( "f is positive.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-1 to +3,
\n" ); document.write( "f is negative.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "+3 to infinity,
\n" ); document.write( "f is positive.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "There is a local minimum somewhere between x at -1 and x at 3. A quick guess might be at or near x=2, meaning this minimum might be $\"-2%2F%284%2B4%2B3%29=-2%2F11\"$ . That means, as a guess, range is -2/11 to ... unsure the maximum without trying some taking of derivatives. (Not very good a guess).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Here is the graph:\r
\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C300%2C-6%2C6%2C-8%2C8%2C%28x%5E2-2x-3%29%2F%28x%5E2%2B2x%2B3%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Some bad guessing having been done as described above, calculus derivative would have been a better method choice. Actual range based on viewing the graph is -1 to +2 for f(x). \n" ); document.write( "

\n" );