If $f: R \rightarrow A$,defined by $f(x) = \cos x + \sqrt{3} \sin x - 1$,is an onto function,then $A =$

The range of $f(x) = \frac{x^2 + 34x - 71}{x^2 + 2x - 7}$ is

The range of the function $f(x) = \frac{e^x \ln x \cdot 5^{(x^2 + 2)}(x^2 - 7x + 10)}{2x^2 - 11x + 12}$ is

Let $f(x)=\sqrt{2-x-x^2}$ and $g(x)=\cos x$. Which of the following statements are true?
$I$. Domain of $f((g(x))^2) = \text{Domain of } f(g(x))$
$II$. Domain of $f(g(x)) + g(f(x)) = \text{Domain of } g(f(x))$
$III$. Domain of $f(g(x)) = \text{Domain of } g(f(x))$
$IV$. Domain of $g((f(x))^3) = \text{Domain of } f(g(x))$

The domain and range of $y(x) = \cos x - 3$ are respectively

If $f:[2,3] \rightarrow R$ is defined by $f(x)=x^3+3x-2$,then the range of $f(x)$ is contained in the interval