document.write( "Question 722950: I have three simple questions about the domain and range of functions:
\n" ); document.write( "1). +sqrt(x-1)
\n" ); document.write( "2). (10^x)+3
\n" ); document.write( "3). Log base 2(x-3)\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "
Algebra.Com's Answer #443029 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
  1. \"sqrt%28x-1%29\"
    • Domain: \"x\" is in the radicand of an even-numbered root (square root is a \"2nd root\"). The radicand of an even-numbered root must not be negative. (IOW: It must be greater than or equal to zero.) So:
      \n" ); document.write( "\"x-1+%3E=+0\"
      \n" ); document.write( "or
      \n" ); document.write( "\"x+%3E=+1\"
      \n" ); document.write( "This is the domain.
    • Range: The expression as a whole is a square root. This cannot be negative, either. So the range is zero and all positive numbers.
  2. \"%2810%5Ex%29%2B3\"
    • Domain: \"x\" is in an exponent. Exponents can be any number. So the domain is all real numbers.
    • Range. A power of 10 can never be zero or negative. (IOW: A power of 10 must be positive.) It can be any positive number. So \"10%5Ex+%3E+0\". If we add three to each side we get: \"10%5Ex+%2B+3+%3E+3\". On the left side we have the expression we started with. So this inequality tells us that the range is all numbers greater than 3.
  3. \"log%282%2C+%28x-3%29%29\"
    • \"x\" is in the argument of a logarithm. Arguments of logarithms must be positive. So
      \n" ); document.write( "x - 3 > 0
      \n" ); document.write( "or
      \n" ); document.write( "x > 3
      \n" ); document.write( "This is the domain.
    • Range: The expression as a whole is a logarithm. The value of a logarithm can be any real number so the range is all real numbers.
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