If a real valued function $f:[a, \infty) \rightarrow[b, \infty)$ defined by $f(x)=2 x^2-3 x+5$ is a bijection. Then, $3 a+2 b=$

The domain of the real valued function $f(x)=\frac{1}{\sqrt{\log _{0.5}(2 x-3)}}+\sqrt{4-9 x^2}$ is

If a function $ f:R \rightarrow R $ is defined by $ f(x) = x^3 - x $, then $ f $ is

If $ f(x) = \sqrt{x - 1} $ and $ g(f(x)) = x + 2x^2 + 1 $, then $ g(x) $ is