Science:Math Exam Resources/Courses/MATH110/December 2014/Question 01 (d)/Solution 1

As it's mentioned in the question, $f(x)={\sqrt {x}}$ is a function. In other words, for any input $x$ in the domain, we have exactly one corresponding output $f(x)$.

However, if $f(9)=\pm 3$ is true, it mean that for the input $x=9$, $f$ has two corresponding outputs, which means $f$ is not a function. Since this makes a contradiction, this proves your friend's claim is incorrect.

Indeed, the range of square root function is always non-negative, therefore the correct value should be $f(9)=3$.