Calculus PYQ - AP EAPCET Mathematics

For $x \in R$ if $f(x)=\sqrt{\log _{10}\left(\frac{3-x}{x}\right)}$, then the domain of $f$ is

If $f(x)=x^3-x$ and $g(x)=\sin 2 x$, then $f\left(g\left(\frac{\pi}{12}\right)\right)=$

The function $f(x)=\sqrt{\frac{3 x^2-5 x-2}{2 x^2-7 x+5}}$ has discontinuous points at $x=$

If $f: R \rightarrow R$ defined by

$$f(x)= \begin{cases}\frac{\sin x-\sin \frac{X}{2}}{x}, & x<0 \\ \frac{\sqrt{x^2+x}-\sqrt{x}}{x^{3 / 2}}, & x>0\end{cases}$$

is continuous on $R$, then $f(0)=$

If a real valued function $f$ is defined by $f(x)=\frac{a x+\sqrt{a^2-x^2}}{b x}$, then $f$ is

Let $f(x)$ be a real valued function. If $f^{\prime}(x)$ is a constant for all $x \in R, f(0)=2$ and $f^{\prime}(0)=1$, then