Graphical Interpretation of Continuity

Q. Let f : R $\to$ R be a function. Define g:R $\to$ by g(x) = |f(x)| for all x. Then g is

1. Onto if f is onto
2. One-one if f is one-one
3. Continuous if f is continuous
4. None of these

Q. If $f\left(x\right)=\frac{x}{2}-1$, determine which of the following statement(s) is (are) true on the following interval $[0,\pi ].$

1. $\tan \left(f\right(x\left)\right)$ and $1/f\left(x\right)$ are both continuous
   
2. $\tan \left(f\right(x\left)\right)$ and $1/f\left(x\right)$ are both discontinuous
   
3. $\tan \left(f\right(x\left)\right)$ and $f^{-1}\left(x\right)$ are both continuous
   
4. $\tan \left(f\right(x\left)\right)$ is continuous but $1/f\left(x\right)$ is not.

Q.

Find the number of discontinuities of the given function between x = 0 and x =2.

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