SMO 2008 Senior Round 1 Question 3
SMO · SMO 2008 Senior Round 1
If $f(x)=x^2+\sqrt{1-x^2}$, where $-1\le x\le1$, find the range of $f(x)$.
$\frac12\le f(x)\le1$
$1\le f(x)\le\frac54$
$1\le f(x)\le\frac{1+2\sqrt3}{4}$
$\frac{\sqrt3}{2}\le f(x)\le1$
$\frac12\le f(x)\le\frac{\sqrt3}{2}$