SOLUTION: {{{ f(x)= sqrt(x+5) +3 }}}. How do I find the domain and range without a calculator?

Algebra ->  Rational-functions -> SOLUTION: {{{ f(x)= sqrt(x+5) +3 }}}. How do I find the domain and range without a calculator?       Log On


   

Question 696354: +f%28x%29=+sqrt%28x%2B5%29+%2B3+. How do I find the domain and range without a calculator?
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
You cannot take the square root of a -ve number, so +x%2B5+%3E=+0+
Hence, +x+%3E=+-5+

So the range is +x+%3E=+-5+


+sqrt%28x%2B5%29+ is smallest when +x%2B5+=+0+, ie +x=-5+, for all other values of x (subject to +x+%3E=+-5+ ) then
+x%2B5+%3E+0+ so +sqrt%28x%2B5%29%3E0+
so then +sqrt%28x%2B5%29%2B3+ has a minimum values of 3 when +x=-5+

so the domain is +f%28x%29+%3E=3+ or if you prefer +3+%3C=+f%28x%29+%3C=+infinity+