Question

The range of $f\left(x\right)=\sqrt{x^2+4x+5}$ is

• A. $(-\infty ,\infty )$
• B. $(0,\infty )$
• C. $[1,\infty )$
• D. None of these

Answer 1

The correct option is C $[1,\infty )$

Note that $x^2+4x+5={\left(x+2\right)}^2+1$.

Hence $1\le x^2+4x+5\le \infty$.

$\therefore 1\le \sqrt{x^2+4x+5}\le \infty$.

Hence the range of the function is $\left[1,\infty \right)$.