document.write( "Question 1189264: a) For the given functions 𝑓(𝑥)= x/x-1 and g(x)=-4/x ,find the domain of the
\n" ); document.write( " composite functions 𝑓o𝑔 and 𝑔o𝑓.\r
\n" ); document.write( "\n" ); document.write( "b) Is 𝑓(𝑥)=x^3 invertible? Explain with reason.
\n" ); document.write( " If 𝑓(𝑥) is invertible, find the inverse of 𝑓(𝑥). Also, graph 𝑓 and 𝑓^-1 on the
\n" ); document.write( " same coordinate axes.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #820605 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
a) For the given functions $\"f%28x%29=+x%2F%28x-1%29\"$ and $\"g%28x%29=-4%2Fx\"$ ,find the domain of the
\n" ); document.write( "composite functions $\"f\"$ o $\"g\"$ and $\"g\"$ o $\"+f\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"f+\"$ o $\"g=f%28g%28x%29%29\"$
\n" ); document.write( " $\"f+\"$ o $\"g=f%28-4%2Fx%29\"$
\n" ); document.write( " $\"f+\"$ o $\"g=%28-4%2Fx%29%2F%28-4%2Fx-1%29\"$
\n" ); document.write( " $\"f+\"$ o $\"g=%28-4%2Fx%29%2F%28-%28x+%2B+4%29%2Fx%29\"$
\n" ); document.write( " $\"f+\"$ o $\"g=4%2F%28x+%2B+4%29\"$ \r
\n" ); document.write( "\n" ); document.write( "domain: exclude $\"x\"$ that makes denominator equal to zero which is $\"x=-4\"$
\n" ); document.write( "so, domain is { $\"x\"$ element $\"R\"$ : $\"x%3C%3E-4\"$ }\r
\n" ); document.write( "\n" ); document.write( " $\"g\"$ o $\"f=g%28f%28x%29%29\"$
\n" ); document.write( " $\"g\"$ o $\"f=g%28x%2F%28x-1%29%29\"$
\n" ); document.write( " $\"g\"$ o $\"f=-4%2F%28x%2F%28x-1%29%29\"$
\n" ); document.write( " $\"g\"$ o $\"f=-%284+%28x+-+1%29%29%2Fx\"$ \r
\n" ); document.write( "\n" ); document.write( "domain:{ $\"x\"$ element $\"R\"$ : $\"x%3C%3E0\"$ }\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "b) Is $\"f%28x%29=x%5E3+\"$ invertible? Explain with reason.\r
\n" ); document.write( "\n" ); document.write( "yes, $\"f%28x%29=x%5E3\"$ is invertible\r
\n" ); document.write( "\n" ); document.write( "reason: pass a horizontal line test\r
\n" ); document.write( "\n" ); document.write( "If we take a horizontal line and slide it up and down the graph, it only ever intersects the function in one spot! This means that each output corresponds with exactly one input. In other words, each input has a unique output. The function $\"f%28x%29=x%5E3\"$ is invertible.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If $\"f%28x%29\"$ is invertible, find the inverse of $\"f%28x%29\"$ . Also, graph $\"f\"$ and $\"f%5E-1\"$ on the same coordinate axes.\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E3\"$ ............recall $\"+f%28x%29=y\"$
\n" ); document.write( " $\"y=x%5E3\"$ ..........swap variables
\n" ); document.write( " $\"x=y%5E3\"$ .........solve for $\"y\"$
\n" ); document.write( " $\"y=root%283%2Cx%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"download\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );