The domain of the function $f(x) = \sqrt{25-x^2}+\sqrt{x-2} + \frac{1}{\sqrt{1 - x}}$ is an interval of what width?

Answer 1

The function $\sqrt{25-x^2}$ is defined for $-5\leq x\leq 5$, since $25-x^2$ must be nonnegative. The function $\sqrt{x-2}$ is defined for $x\geq 2$, since $x-2$ must be nonnegative. Lastly, the function $\frac{1}{\sqrt{1-x}}$ is defined for $x<1$, since $1-x$ must be positive. Therefore, the function $f(x) = \sqrt{25-x^2}+\sqrt{x-2} + \frac{1}{\sqrt{1 - x}}$ is defined for $x<1$ and $x\geq2$.

The width of this interval is $\boxed{\infty}$.