document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165630>Question 1165630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> g={(-4,-9),(-2,8),(4,5),(8,4)}\r<BR>\n" );
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document.write( "h(x)=2x-13\r<BR>\n" );
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document.write( "Find the following<BR>\n" );
document.write( "g^-1(8)=<BR>\n" );
document.write( "h^-1(x)=<BR>\n" );
document.write( "(h∘h^-1)(-5)= </SPAN>\n" );
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document.write( "g={(-4,-9),(-2,8),(4,5),(8,4)}<BR>\n" );
document.write( "h(x)=2x-13<br><BR>\n" );
document.write( "(1) Find g^(-1)(8)<br><BR>\n" );
document.write( "Here we are asked to find \"g inverse of 8\".  By the definition of inverse functions, that is the input value that produces an output value of 8.<br><BR>\n" );
document.write( "By inspection of the definition of the function g, the answer is -2.<br><BR>\n" );
document.write( "ANSWER: -2<br><BR>\n" );
document.write( "(2) Find h^(-1)(x)<br><BR>\n" );
document.write( "Here we are asked to find the inverse of the given function h. The standard process for finding the inverse of a function is as shown in the other response to your post: switch the x and y and solve for the new y.<br><BR>\n" );
document.write( "For simple functions like the given h(x), an easier and faster way is to use the concept that an inverse function \"gets you back where you started\". To get back where you started, you need to \"retrace your steps\", which means perform the opposite operations in the opposite order.<br><BR>\n" );
document.write( "In this example, the given function performs the following operations: multiply by 2; add 13. So the inverse function must perform the following operations: subtract 13; divide by 2.<br><BR>\n" );
document.write( "ANSWER: (x-13)/2<br><BR>\n" );
document.write( "(3) Find (h∘h^-1)(-5)<br><BR>\n" );
document.write( "Again, by definition, an inverse function \"gets you back where you started\".  So operating on a given input by the inverse of a function and then operating on the result by the original function gets you back where you started.<br><BR>\n" );
document.write( "ANSWER: (h∘h^-1)(-5) = -5<br><BR>\n" );
document.write( " </SPAN>\n" );
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