document.write( "Question 87625: Given the functions f(x)=sqrt-3x+15 and g(x)=5/x, determine g * f(x) and find its domain. \r
\n" ); document.write( "\n" ); document.write( "*please note that the question has a small o where I have placed an * symbol. I am not sure what that means.\r
\n" ); document.write( "\n" ); document.write( "Please someone help me. \n" ); document.write( "
Algebra.Com's Answer #63525 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
Given:\"f%28x%29+=+sqrt%28-3x%2B15%29\" and \"g%28x%29+=+5%2Fx\", determine \"%28g%5B0%5Df%29%28x%29\"
\n" ); document.write( "What you are being asked to determine is \"the composite of g and f\"
\n" ); document.write( "This can also shown be as \"g%28f%28x%29%29\"
\n" ); document.write( "These are both read as \"g of f of x\" and it is really a function of a function.
\n" ); document.write( "Here's how it works:
\n" ); document.write( "You are given that: \"f%28x%29+=+sqrt%28-3x%2B15%29\" so when you are asked for g(f(x)) you are being asked for: \"g%28sqrt%28-3x%2B15%29%29\" so in the function \"g%28x%29+=+%285%2Fx%29\" you would substitute \"x+=+sqrt%28-3x%2B15%29\" to get:
\n" ); document.write( "\"g%28f%28x%29%29+=+5%2Fsqrt%28-3x%2B15%29\" \r
\n" ); document.write( "\n" ); document.write( "You are also being asked to find the domain which is the set of all possible values of the independent variable, in this case, that's x.
\n" ); document.write( "You have to look at the denominator of the composite \"sqrt%28-3x%2B15%29\" to see that, if x were equal to 5, the the denominator would becom zero, and this is not permissable because division by zero is undefined..
\n" ); document.write( "So x = 5 is an excluded value of the domain.
\n" ); document.write( "Also you should notice that if x > 5, the denominator would become a complex number \"%28ai%2Bb%29\" so it looks like the domain, x, can be any real number that is less than 5, or x < 5.\r
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