What is the \(x\)-coordinate of the point of intersection of the graphs \(y=\sqrt{x}\) and \(y=x-2\)?

Correct answer: \(x=4\)

At an intersection, the two functions have the same \(y\)-value, so \(\sqrt{x}=x-2\). Since the left side is non-negative, we must have \(x-2\ge 0\), hence \(x\ge 2\). Squaring gives \(x=(x-2)^2\), or \(x^2-5x+4=0\), whose roots are \(x=1\) and \(x=4\). However, \(x=1\) violates the condition \(x\ge 2\) and is an extraneous root introduced by squaring. Therefore, \(x=4\); checking gives \(\sqrt{4}=2=4-2\). Exam tip: Always substitute the roots back into the original equation after squaring.