Practicing Success
Let $f(x)=\cos^{-1}\left(\frac{x^2}{1+x^2}\right)$. The range of f is |
$\left[0,\frac{π}{2}\right]$ $\left[-\frac{π}{2},\frac{π}{2}\right]$ $\left[-\frac{π}{2},0\right]$ none of these |
none of these |
$\left(\frac{x^2}{1+x^2}\right)≤1$ This is true for all x ∈ R. So, the domain = R Now, $\frac{x^2}{1+x^2}=1-\frac{1}{1+x^2}$ $∴ 0≤\frac{x^2}{1+x^2}<1;\cos^{-1}0≥\cos^{-1}\frac{x^2}{1+x^2}>\cos^{-1}1⇒\frac{π}{2}≥\cos^{-1}\frac{x^2}{1+x^2}>0$ ∴ the range = $\left(0,\frac{π}{2}\right]$ |