Medium Practice — Set 2

Quick Recap — Functions in Depth

• Domain rules: even roots need $\ge0$; logs need $>0$; denominators $\ne0$.
• Range via completing the square, or writing $y=f(x)$ and demanding real $x$ (discriminant).
• Composition & inverse: $(f\circ g)$, $f^{-1}$ exists for bijections; $(f^{-1})^{-1}=f$.
• Periodic functions: $\sin,\cos$ period $2\pi$; $\tan$ period $\pi$; $|{\sin x}|$ period $\pi$.