The range of the real valued function $f(x)=\frac{15}{3 \sin x+4 \cos x+10}$ is

Define the function, $f, g$ and $h$ from $R$ to $R$ such that $f(x)=x^2-1, g(x)=\sqrt{x^2+1}$ and $h(x)= \begin{cases}0, \text { if } & x \leq 0 \\ x, \text { if } & x \geq 0\end{cases}$ consider the following statements

(i) fog is invertible

(ii) $h$ is an identify function

(iii) $f \circ g$ is not invertible

(iv) $(h \circ f \circ g) x=x^2$

Then, which one of the following is true ?

The domain of the real valued function $f(x)=\sqrt{9-\sqrt{x^2-144}}$ is

The real valued function $f: R \rightarrow\left[\frac{5}{2}, \infty\right)$ defined by $f(x)=|2 x+1|+|x-2|$ is