anonymous
  • anonymous
Determine the domain of the function. f(x) is equal to the square root of two minus x. x ≤ 2 All real numbers x > 2 All real numbers except 2
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[f(x)=\sqrt{2-x}\]
jim_thompson5910
  • jim_thompson5910
Hint: You cannot take the square root of a negative number (and get some real number)
jim_thompson5910
  • jim_thompson5910
So the radicand (the stuff inside the square root) can't be negative

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anonymous
  • anonymous
can you please teach me how to do this step by step PLEASE
jim_thompson5910
  • jim_thompson5910
Similar example: Find the domain of \[\Large g(x) = \sqrt{x+3}\] You can't take the square root of a negative number, so the radicand must be either 0 or positive. So... \[\Large x+3 \ge 0\] \[\Large x+3-3 \ge 0-3\] \[\Large x \ge -3\] is the domain
anonymous
  • anonymous
but its positive ??
jim_thompson5910
  • jim_thompson5910
I'm not sure what you mean
anonymous
  • anonymous
you said you can't take the square root of a negative number
jim_thompson5910
  • jim_thompson5910
yes exactly, so whatever number that is in the square root is either a) zero or b) positive
anonymous
  • anonymous
if your finding the domain of a square root your rules are that the number cant be negative. if you were taking the domain of a fraction the rules would be you cant have a zero on the denominator
anonymous
  • anonymous
is the answer x ≤ 2
ganeshie8
  • ganeshie8
correct! good work !!
anonymous
  • anonymous
i missed you @ganeshie8

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