document.write( "Question 1084544: given f(x)=√2x-1 and g(x)= x^2+1,x grater then or equal to 0\r
\n" ); document.write( "\n" ); document.write( "1.without finding the formula for f^-1,find f^-1(5)
\n" ); document.write( "2.find f^-1(x) and g^-1(x)
\n" ); document.write( "3.give range of f^-1(x) and give the domain of g^-1(x)
\n" ); document.write( "4.express (g o f)(x) in simplified form \n" ); document.write( "
Algebra.Com's Answer #698652 by MathLover1(20850)\"\" \"About 
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\n" ); document.write( "given \"f%28x%29=sqrt%282x-1%29+\"and \"g%28x%29=+x%5E2%2B1\", where \"x+%3E=0\"\r
\n" ); document.write( "\n" ); document.write( "1.without finding the formula for \"f%5E-1\",find\"+f%5E-1%285%29\"\r
\n" ); document.write( "\n" ); document.write( "Determining the value of \"+f%5E-1%285%29\" is equivalent to determining the \"x\"
\n" ); document.write( "value when \"+f%28x%29=5\"\r
\n" ); document.write( "\n" ); document.write( "\"5=sqrt%282x-1%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"5%5E2=%28sqrt%282x-1%29+%29%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"25=2x-1\"\r
\n" ); document.write( "\n" ); document.write( "\"25%2B1=2x\"\r
\n" ); document.write( "\n" ); document.write( "\"26%2F2=x\"\r
\n" ); document.write( "\n" ); document.write( "\"x=13\"\r
\n" ); document.write( "\n" ); document.write( "\"+f%5E-1%285%29=13\"\r
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\n" ); document.write( "\n" ); document.write( "2.find \"f%5E-1%28x%29\" and \"g%5E-1%28x%29\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29=sqrt%282x-1%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"y=sqrt%282x-1%29+\".............swap \"x\" and \"y\"\r
\n" ); document.write( "\n" ); document.write( "\"x=sqrt%282y-1%29+\".......solve for \"y\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2=%28sqrt%282y-1%29%29%5E2+\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2=2y-1+\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B1=2y+\"\r
\n" ); document.write( "\n" ); document.write( "\"%281%2F2%29%28x%5E2%2B1%29=y+\"\r
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\n" ); document.write( "\n" ); document.write( "\"f%5E-1%28x%29=%281%2F2%29%28x%5E2%2B1%29\"\r
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\n" ); document.write( "\n" ); document.write( " \"g%28x%29=+x%5E2%2B1\"\r
\n" ); document.write( "\n" ); document.write( " \"y=+x%5E2%2B1\"\r
\n" ); document.write( "\n" ); document.write( " \"x=+y%5E2%2B1\"\r
\n" ); document.write( "\n" ); document.write( " \"x-1=+y%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"y=sqrt%28x-1%29\"\r
\n" ); document.write( "\n" ); document.write( "\"g%5E-1%28x%29=sqrt%28x-1%29\"\r
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\n" ); document.write( "\n" ); document.write( "3.give range of f^-1(x) and give the domain of g^-1(x)\r
\n" ); document.write( "\n" ); document.write( "\"f%5E-1%28x%29=x%5E2%2B1\"\r
\n" ); document.write( "\n" ); document.write( "domain: \"R\" (all real numbers)\r
\n" ); document.write( "\n" ); document.write( "(\"-infinity\",\"infinity\")
\n" ); document.write( "range: { \"y\" element \"R\" : \"y%3E=1\" }
\n" ); document.write( "[\"1\",\"infinity\")\r
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\n" ); document.write( "\n" ); document.write( "4.express \"%28g+o+f%29%28x%29\" in simplified form \r
\n" ); document.write( "\n" ); document.write( "I usually convert \"%28+f+o+g%29%28x%29\" to the more intuitive \"+f+%28g%28x%29%29\" :\r
\n" ); document.write( "\n" ); document.write( " \"+f+%28g%28x%29%29=f%28+x%5E2%2B1%29\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28+x%5E2%2B1%29=sqrt%282%28+x%5E2%2B1%29-1%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28+x%5E2%2B1%29=sqrt%282x%5E2%2B2-1%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28+x%5E2%2B1%29=sqrt%282x%5E2%2B1%29+\"\r
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