Identity the Identity function, if any.

Find $f\left(\sqrt{2}\right)$ and $f\left(-\sqrt{3}\right)$ for the function $f\left(x\right)=\left\{\begin{array}{l}{x}^2 \mathrm{if} x<0\\ x \mathrm{if} 0\le x\le 1\\ \frac{1}{x} \mathrm{if} x>1\end{array}\right.$

Find $x$ for which the value of $f\left(x\right)=x^2-4x+3$ is equal to $0$

Find $x$ for which the value of $f\left(x\right)=x^2-4x+3$ is equal to $-1$

Find the value/values of $x$ for which the following functions are not defined:

(i) $\frac{x^2-4}{x-2}$

Find the value/values of $x$ for which the following functions are not defined:

(ii) $\frac{\sin x}{x}$

Find the value/values of $x$ for which the following functions are not defined:

(iii) $\frac{\log \cos x}{\sec x}$

Let $f\left(x\right)=\sqrt{1+x}, g\left(x\right)=\sqrt{1-x}$

find $f+g$

Also find the domain in each case.

Let $f\left(x\right)=\sqrt{1+x}, g\left(x\right)=\sqrt{1-x}$

find $f-g$

Also find the domain in each case.