document.write( "Question 1094396: Let f(x) = 3x-2 and g(x) = 5/(3x), for x does not equal 0.
\n" ); document.write( "Find f^-1(x).
\n" ); document.write( "Show that ( g ° f^-1) (x) = 5/(x+2).
\n" ); document.write( "Let h(x) = 5/x+2, for x is greater or equal to 0. The graph of h has a horizontal asymptote at y=0.
\n" ); document.write( "Find the y-intercept of the graph of h.
\n" ); document.write( "Hence, sketch the graph of h.
\n" ); document.write( "Find the graph of h^-1, write down the x-intercept.
\n" ); document.write( "For the graph of h^-1, write down the equation of the vertical asymptote.
\n" ); document.write( "Given that h^-1(a)=3, find the value of a. \n" ); document.write( "
Algebra.Com's Answer #708968 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let f(x) = 3x-2 and g(x) = \"5%2F%283x%29\", for x does not equal 0.\r\n" );
document.write( "Find f-1(x).\r\n" );
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document.write( "1. In place of f(x), replace it by y\r\n" );
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document.write( "y = 3x-2\r\n" );
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document.write( "2. Interchange x and y\r\n" );
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document.write( "x = 3y-2\r\n" );
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document.write( "3. Solve for y\r\n" );
document.write( "   x = 3y-2\r\n" );
document.write( "3y-2 = x          <--swap sides\r\n" );
document.write( "  3y = x+2\r\n" );
document.write( "   y = \"%28x%2B2%29%2F3\"\r\n" );
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document.write( "4. In place of y, replace it by f-1(x)\r\n" );
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document.write( "f-1(x) = \"%28x%2B2%29%2F3\"  \r\n" );
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document.write( "Show that (g∘f-1)(x) = \"5%2F%28x%2B2%29\".\r\n" );
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document.write( "g(x) = \"5%2F%283x%29\"\r\n" );
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document.write( "To avoid so many fractions, rewrite using \"÷\"\r\n" );
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document.write( "g(x) = \"matrix%281%2C3%2C5%2C%22%F7%22%2C3x%29\"\r\n" );
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document.write( "In place of x, replace it by the right side of f-1(x),\r\n" );
document.write( "which is {{(x+2)/2}}}\r\n" );
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document.write( "(g∘f-1)(x) = \"matrix%281%2C3%2C5%2C%22%F7%22%2C3%28%28x%2B2%29%2F3%29%29%29\"\r\n" );
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document.write( "(g∘f-1)(x) = \"matrix%281%2C3%2C5%2C%22%F7%22%2Ccross%283%29%28%28x%2B2%29%2Fcross%283%29%29%29%29\"\r\n" );
document.write( "(g∘f-1)(x) = \"matrix%281%2C3%2C5%2C%22%F7%22%2Cx%2B2%29\"\r\n" );
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document.write( "(g∘f-1)(x) = \"5%2F%28x%2B2%29\"\r\n" );
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\n" ); document.write( "Let h(x) = \"5%2F%28x%2B2%29\", for x≧0. The graph of h has a horizontal
\n" ); document.write( "asymptote at y=0.
\n" ); document.write( "Find the y-intercept of the graph of h.
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document.write( "We let x equal to 0\r\n" );
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document.write( "h(0) = \"5%2F%280%2B2%29\"\r\n" );
document.write( "h(0) = \"5%2F2\"\r\n" );
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document.write( "So the y-intercept is the point \"%28matrix%281%2C3%2C0%2C%22%2C%22%2C5%2F2%29%29\"\r\n" );
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document.write( "Hence, sketch the graph of h. \r\n" );
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document.write( "Since x≧0, the graph starts at the y-intercept and goes to the\r\n" );
document.write( "right.  The graph does not extend left of the y-intercept:\r\n" );
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document.write( "You do the rest by yourself.  If you have trouble, tell me in\r\n" );
document.write( "the thank you note form below, and I will get back to you by\r\n" );
document.write( "email. \r\n" );
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document.write( "Edwin
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