Functions $\mathrm{f}$ and $\mathrm{g}$ are defined by $\mathrm{f}:x\mapsto \left| x+1 \right|$, $x\

Question

Functions $\mathrm{f}$ and $\mathrm{g}$ are defined by $\mathrm{f}:x\mapsto \left| x+1 ight|$, $x\in \mathbb{R}$ $\mathrm{g}:x\mapsto \ln ({{x}^{2}})$, $x\in \mathbb{R}$, $x
e 0$ Sketch the graphs of $\mathrm{f}$ and $\mathrm{g}$, and state the range of each function. Explain why $\mathrm{fg}$ exists, define $\mathrm{fg}$ and state its range. Using a graphical approach, solve the inequality $\mathrm{fg}(x)-\mathrm{f}(x)>0$.

Accepted Answer

(i) ${\mathbb{R}_0^+}$ ,$\mathbb{R}$ (ii) $\mathbb{R}_{0}^{+}$ (iii) $-5.36 < x < -0.703$ 	ext{ or } $-0.464 < x < 0$ 	ext{ or } $0< x < 0.314$

RI Functions Tutorial Q6

RI Functions Tutorial Q6

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