Practicing Success
Practicing Success
CUET Preparation Today
Find the range of the function $f(x)=\sin^{-1}((1+e^x)^{-1})$. |
$(-\frac{π}{2},\frac{π}{2})$ $(0,\frac{π}{2})$ $(-\frac{π}{2},1)$ $(\frac{π}{2},\frac{π}{2})$ |
$(0,\frac{π}{2})$ |
$e^x∈(0,∞)$ $e^x+1∈(1,∞)$ $(e^x+1)^{-1}∈(0,1)$ so $\sin^{-1}(e^x+1)^{-1}∈(0,\frac{π}{2})$ |
