The domain of a function $f(y)=\frac{\cos ^{-1}(y-5)}{\sqrt{25-y^{2}}}$ is
The domain of a function $f(y)=\frac{\cos ^{-1}(y-5)}{\sqrt{25-y^{2}}}$ is
$(4,6]$
$(-5,5)$
$[4,5)$
$(4,5]$
Solution
We have $f(y)=\frac{\cos ^{-1}(y-5)}{\sqrt{25-y^{2}}}$
Here $-1 \leq y-5 \leq 1$ and $25-y^{2}>0$ $\therefore \quad 4 \leq y \leq 6 \quad$ and $\quad-5 < y < 5$ Hence domain of $f(y)$ is $[4,5)$