document.write( "Question 1026181: 6. (a) Find the domain of the function
\n" ); document.write( "f(x) = {x / sqrt (5−3x) + x sqrt (x + 1)}
\n" ); document.write( "(b) Consider f(x) = sqrt (4x^2 + 1 ) and g(x) = x + 3/ x^2 . Find the composite functions f ◦g and g◦f.
\n" ); document.write( "(c) Consider h(x) = x^3 + 5 and k(x) = x^4 + 2x + 3. Find function l such that h◦l = k. \n" ); document.write( "

Algebra.Com's Answer #641439 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "6. (a) Find the domain of the function
\n" ); document.write( "f(x) = {x / sqrt (5-3x) + x sqrt (x + 1)}
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document.write( "When you see a square root, and you are asked about the domain, take care that the function under the square root is non-negative.\r\n" );
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document.write( "So, in this case these two inequalities must be held:\r\n" );
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document.write( "5-3x > 0,    (1)   and\r\n" );
document.write( "x+1   = 0.   (2).\r\n" );
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document.write( "Notice that in (1) I wrote the strong inequality.\r\n" );
document.write( "It is because we have  in the denominator.\r\n" );
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document.write( "Now, from (1),  5 > 3x,  x < .\r\n" );
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document.write( "From (2),  x >= -1.\r\n" );
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document.write( "So, the answer is -1 <= x < .\r\n" );
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document.write( "It is the semi-segment  [-1, ).\r\n" );
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document.write( "The domain is the semi-segment  [-1, ).\r\n" );
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